Olivier Menoukeu-Pamen

• University of Liverpool

In this paper, we study the problem of stochastic optimal control for systems governed by stochastic differential equations (SDEs) with drift coefficients of bounded variation. We establish both necessary and sufficient stochastic maximum principle. To achieve this, we prove the existence and uniqueness of solutions to SDEs with random drifts of bo...

In this article, we construct unique strong solutions to a class of stochastic Volterra differential equations driven by a singular drift vector field and a Wiener noise. Further, we examine the Sobolev differentiability of the strong solution with respect to its initial value.

We investigate the convergence rate for the time discretization of a class of quadratic backward SDEs-potentially involving path-dependent terminal values-when coupled with non-standard Lipschitz-type forward SDEs. In our review of the explicit time-discretization schemes in the spirit of Pagès & Sagna (see [43]), we achieve an error control close...

This paper develops multistate models to analyse loan delinquency in the microfinance sector, using data from Ghana. The models are designed to account for both partial repayments and the short repayment durations typical in microfinance, focusing on estimating the probability of transitions between two or three repayment states, including delinque...

In this paper, we investigate a complex variation of the standard joint life annuity policy by introducing three distinct contingent benefits for the surviving member(s) of a couple, along with a contingent benefit for their beneficiaries if both members pass away. Our objective is to price this innovative insurance policy and analyse its sensitivi...

We formulate a stochastic differential equation(SDE) model from a deterministic model of imperfect vaccination building on a recent analytical approach of Allen et al [5], which derivation procedure is based on the elementary events occurring during the epidemiological dynamics and their corresponding probabilities. We prove the global existence of...

We explore the existence of a continuous marginal law with respect to the Lebesgue measure for each component $(X,Y,Z)$ of the solution to coupled quadratic forward--backward stochastic differential equations (QFBSDEs) {for which the drift coefficient of the forward component is either bounded and measurable or H\"older continuous. Our approach rel...

This paper investigates mathematical modeling and numerical methods for simulations of the input–output behavior of a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. There, a given volume under or aside of a building is filled...

We explore the existence of a continuous marginal law with respect to the Lebesgue measure for each component (X, Y, Z) of the solution to coupled quadratic forward-backward stochastic differential equations (QFBSDEs) for which the drift coefficient of the forward component is either bounded and measurable or Hölder continuous. Our approach relies...

We prove the existence of a unique Malliavin differentiable strong solution to a stochastic differential equation on the plane with merely integrable coefficients driven by the fractional Brownian sheet with Hurst parameter $H=(H_1,H_2)\in(0,\frac{1}{2})^2$. The proof of this result relies on a compactness criterion for square integrable Wiener fun...

In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first derive an explicit representation of the first variation process (in the Sobolev sense) of the controlled diffu...

Vaccination is an essential tool for the management of infectious diseases. However, many vaccines are imperfect, having only a partial protective effect in decreasing disease transmission and/or favouring recovery of infected individuals and possibly exhibiting a trade-off between these two properties. Furthermore, the success of vaccination also...

Interest rates frequently exhibit regulated or controlled characteristics, for example, the prevailing zero interest rate policy, or the leading role of central banks in short rate markets. In order to capture the regulated dynamics of interest rates, we introduce the skew constant-elasticity-of-variance (skew CEV) model. We then propose two numeri...

In this paper we are interested in a quasi-linear hyperbolic stochastic differential equation (HSPDE) when the vector field is merely bounded and measurable. Although the deterministic counterpart of such equation may be ill-posed (in the sense that uniqueness or even existence might not be valid), we show for the first time that the corresponding...

In this paper, we consider quadratic forward-backward SDEs (QFBSDEs), for which the drift in the forward equation does not satisfy the standard globally Lipschitz condition and the driver of the backward system possesses nonlinearity of type f (|y|)|z| 2 , where f is any locally integrable function. We prove both the Malliavin and classical derivat...

We prove path-by-path uniqueness of solution to hyperbolic stochastic partial differential equations when the drift coefficient is the difference of two componentwise monotone Borel measurable functions of spatial linear growth. The Yamada-Watanabe principle for SDE driven by Brownian sheet then allows to derive strong uniqueness for such equation...

In this paper we present an iterative optimal stopping method for general optimal stopping problems for Feller processes. We show using an approximating scheme that the value function of an optimal stopping problem for some general operator is the unique viscosity solution to an Hamilton–Jacobi-Bellman equation (see for example Theorem 2.3, Theorem...

In this paper we study path-by-path uniqueness for multidimensional stochastic differential equations driven by the Brownian sheet. We assume that the drift coefficient is unbounded, verifies a spatial linear growth condition and is componentwise nondeacreasing. Our approach consists of showing the result for bounded and componentwise nondecreasing...

In this paper we study path-by-path uniqueness for multidimensional stochastic differential equations driven by the Brownian sheet. We assume that the drift coefficient is unbounded, verifies a spatial linear growth condition and is componentwise nondeacreasing. Our approach consists of showing the result for bounded and componentwise nondecreasing...

The main objective of this work is to propose concrete time reduction strategies for discovery of Wi-Fi Direct in Android. To achieve our goals, we perform a fairly general mathematical modeling of the discovery of devices using Poisson processes. Subsequently, under asymptotic invariance hypotheses of certain distributions, we derive formulas for...

Vaccination is essential for the management of infectious diseases, many of which continue to pose devastating public health and economic challenges across the world. However, many vaccines are imperfect having only a partial protective effect in decreasing disease transmission and/or favouring recovery of infected individuals, and possibly exhibit...

In this paper, we study the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana during its initial phase by using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, ℛ0, for the proposed model is 1.04. One of the main focus of this study is global stability results. Theoretically a...

In this work, we prove strong convergence on small time interval of order 1/2-\epsilon for arbitrarily small \epsilon>0 of the Euler-Maruyama approximation for additive Brownian motion with Holder continuous drift satisfying a linear growth condition. The proof is based on direct estimations of functional of the Euler-Maruyama approximation. The or...

In this work, we study a class of quadratic forward backward stochastic differential equations (QFBSDEs) with measurable drift and continuous generator. We establish some existence and uniqueness results for such QFBSDEs. Our approach is based on a weak decoupling field and an Itô-Krylov formula for BSDE. In the one dimensional case, we derive exis...

This paper investigates solvability of fully coupled systems of forward–backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and bounded in the forward process. We crucially use compactness results from the theory of Malliavin calculus to...

In this work, we generalise the stochastic local time space integration introduced in \cite{Ei00} to the case of Brownian sheet. %We develop a stochastic local time-space calculus with respect to the Brownian sheet. This allows us to prove a generalised two-parameter It\^o formula and derive Davie type inequalities for the Brownian sheet. Such esti...

We investigate Takagi-type functions with roughness parameter $\gamma$ that are H\"older continuous with coefficient $H=\frac{\log\gamma}{\log \eh}.$ Analytical access is provided by an embedding into a dynamical system related to the baker transform where the graphs of the functions are identified as their global attractors. They possess stable ma...

The main objective of this work is to propose concrete time reduction strategies for discovery of Wi-Fi Direct in Android. To achieve our goals, we perform a fairly general mathematical modeling of the discovery of devices using Poisson processes. Subsequently, under asymptotic invariance hypotheses of certain distributions, we derive formulas for...

This paper is devoted to numerical simulations of the short-term behavior of the spatial temperature distribution in a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. We apply numerical methods derived in our companion paper [8...

This paper investigates numerical methods for simulations of the short-term behavior of a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. There a given volume under or aside of a building is filled with soil and insulated to th...

In this paper, we present the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana, using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, R0, for the proposed model is 1.04. One of the main focus of this study is stability results and senesitity assessment of the parameters. We...

In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first derive an explicit representation of the first variation process (in Sobolev sense ) of the controlled diffusio...

We investigate Weierstrass functions with roughness parameter $\gamma$ that are H\"older continuous with coefficient $H={\log\gamma}/{\log \frac12}.$ Analytical access is provided by an embedding into a dynamical system related to the baker transform where the graphs of the functions are identified as their global attractors. They possess stable ma...

Broken-heart syndrome is the most common form of short-term dependence, inducing a temporary increase in an individual’s force of mortality upon the occurrence of extreme events, such as the loss of a spouse. Socioeconomic influences on bereavement processes allow for suggestion of variability in the significance of short-term dependence between co...

This paper investigates a fully probabilistic method for the well-posedness of second order quasilinear parabolic equations with rough coefficients. The equations are considered in the $L^p$-viscosity sense. The method of proof relies on the investigation of \emph{strong} solutions of associated fully coupled systems of forward and backward stochas...

In this paper we review and improve pathwise uniqueness results for some types of one-dimensional stochastic differential equations (SDE) involving the local time of the unknown process. The diffusion coefficient of the SDEs we consider is allowed to vanish on a set of positive measure and is not assumed to be smooth. As opposed to various existing...

The African Institute for Mathematical Sciences (AIMS) Ghana invites applications for the 1st Edition of the Colloquium of Ph.D Candidates in Mathematics and its Applications (CMiA), scheduled from November 4-7, 2019 at AIMS Ghana in Accra. To increase cooperation among researchers, the colloquium is organized within the framework of the German Res...

In this paper, we pursue the optimal reinsurance-investment strategy of an insurer who can invest in both domestic and foreign markets. We assume that both the domestic and the foreign nominal interest rates are described by extended Cox-Ingersoll-Ross (CIR) models. In order to hedge the risk associated to investments, rolling bonds, treasury infla...

In this paper, we are interested in the following forward stochastic differential equation (SDE) $$ d X_{t}=b(t,\omega,X_{t})dt +\sigma d B_{t}\quad 0\leq t\leq T,\quad X_{0}=x\in \mathbb{R}, $$ where the coefficient $b:[0,T] \times \mathbb{R}\times \Omega\longrightarrow \mathbb{R}$ is Borel measurable and of linear growth in the second variable an...

We study two applications of spatial Sobolev smoothness of stochastic flows of unique strong solution to stochastic differential equations (SDEs) with irregular drift coefficients. First, we analyse the stochastic transport equation assuming that the drift coefficient is Borel measurable, with spatial linear growth and show that the above equation...

This paper studies partially observed risk-sensitive optimal control problems with correlated noises between the system and the observation. It is assumed that the state process is governed by a continuous-time Markov regime-switching jump-diffusion process and the cost functional is of an exponential-of-integral type. By virtue of a classical spik...

We study an optimal stopping problem when the state process is governed by a general Feller process. In particular, we examine viscosity properties of the associated value function with no a priori assumption on the stochastic differential equation satisfied by the state process. Our approach relies on properties of the Feller semigroup. We present...

In this paper we review and improve pathwise uniqueness results for some types of one-dimensional stochastic differential equations (SDE) involving the local time of the unknown process. The diffusion coefficient of the SDEs we consider is allowed to vanish on a set of positive measure and is not assumed to be smooth. As opposed to various existing...

This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward-backward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for optimal control for a system driven by a Markov regime-switching forward and backward jump-diffusion model is...

In the present work, we consider an optimal control for a three-factor stochastic factor model. We assume that one of the factors is not observed and use classical filtering technique to transform the partial observation control problem for stochastic differential equation (SDE) to a full observation control problem for stochastic partial different...

In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps and partial information. First, we prove a sufficient maximum principle for non zero-sum stochastic differential game problems and obtain equilibrium point for such games....

In this paper, we explore two new tree lattice methods, the piecewise binomial tree and the piecewise trinomial tree for both the bond prices and European/American bond option prices assuming that the short rate is given by a generalized skew Vasicek model with discontinuous drift coefficient. These methods build nonuniform jump size piecewise bino...

In this paper, we derive a general stochastic maximum principle for a risk-sensitive type optimal control problem of Markov regime-switching jump-diffusion model. The results are obtained via a logarithmic transformation and the relationship between adjoint variables and the value function. We apply the results to study both a linear-quadratic opti...

In this paper, we are interested in the following singular stochastic differential equation (SDE) \begin{equation*} \diffns X_{t}=b(t,X_{t}) \diffns t +\diffns B_{t},\,\,\,0\leq t\leq T,\,\,\,\text{ }X_{0}=\,x\in \mathbb{R% }^{d}, \end{equation*} where the drift coefficient $b:[0,T]\times \mathbb{R}^{d}\longrightarrow \mathbb{R}^{d}$ is Borel measu...

In this paper, we are interested in the following singular stochastic differential equation (SDE) $${\rm d} X_t = b(t,X_t) {\rm d} t + {\rm d} B_{t},\ 0\leq t\leq T,\ X_0 = x \in \mathbb{R}^d,$$ where the drift coefficient $b:[0,T]\times \mathbb{R}^{d}\longrightarrow \mathbb{R}^{d}$ is Borel measurable, possibly unbounded and has spatial linear gro...

In this paper, we study option pricing under a regime-switching exponential Lévy model. Assuming that the coefficients are time-dependent and modulated by a finite state Markov chain, we generalise the work in Momeya and Morales (Method Comput Appl Probab, 2014, doi:10.1007/s11009-014-9399-2), and Siu and Yang (Acta Mathe Appl Sin 2:369–388, 2009),...

In 1988 Dybvig introduced the payoff distribution pricing model (PDPM) as an alternative to the capital asset pricing model (CAPM). Under this new paradigm agents preferences depend on the probability distribution of the payoff and for the same distribution agents prefer the payoff that requires less investment. In this context he gave the notion o...

In 1988 Dybvig introduced the payo distribution pricing model (PDPM) as an alternative to the capital asset pricing model (CAPM). Under this new paradigm agents preferences depend on the probability distribution of the payo and for the same distribution agents prefer the payo that requires less investment. In this context he gave the notion of ecie...

In 1988 Dybvig introduced the payoff distribution pricing model (PDPM) as an alternative to the capital asset pricing model (CAPM). Under this new paradigm agents preferences depend on the probability distribution of the payoff and for the same distribution agents prefer the payoff that requires less investment. In this context he gave the notion o...

In this paper, we study a robust recursive utility maximization problem for time-delayed stochastic differential equation with jumps. This problem can be written as a stochastic delayed differential game. We suggest a maximum principle of this problem and obtain necessary and sufficient condition of optimality. We apply the result to study a proble...

In this paper, we consider the following singular stochastic differential equation (SDE) $$X_t=x_0+ \int_0^t b(s, X_s)ds + L_t,~x_0 \in \mathbb{R}^d,~t \in [0,T],$$ where the drift coefficient $b:[0,T] \times \mathbb{R}^d \to \mathbb{R}^d$ is H\"older continuous in both time and space variables and the noise $L=(L_t)_{0 \leq t \leq T}$ is a $d$-dim...

In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) $$X_{t}=x_{0}+ \int_{0}^{t} b(s, X_{s}) \mathrm{d}s + L_{t},~x_{0} \in \mathbb{R}^{d},~t \in [0,T],$$ where the drift coefficient $b:[0,T] \times \mathbb{R}^d \to \mathbb{R}^d$ is H\"older continuous in both time and space variables and the noise $L=(...

We prove an existence and uniqueness result for non-linear time-advanced backward stochastic partial differential equations with jumps (ABSPDEJs). We then apply our results to study a time-advanced backward type of stochastic generalized porous medium equations with jumps.

In this paper, the option hedging problem for a Markov-modulated exponential Lévy model is examined. We use the local risk-minimization approach to study optimal hedging strategies for Europeans derivatives when the price of the underlying is given by a regime-switching Lévy model. We use a martingale representation theorem result to construct an e...

In the present work, a stochastic maximum principle for discounted control of a certain class of degenerate diffusion processes with global Lipschitz coefficient is investigated. The value function is given by a discounted performance functional, leading to a stochastic maximum principle of semi-couple forward–backward stochastic differential equat...

In this paper, we study the optimization problem confronted by an insurance �rm whose management can control its cash-balance dynamics by adjusting the underlying premium rate. The �rm's objective is to minimize the total deviation of its cash-balance process to some pre-set target levels by selecting an appropriate premium policy. We study the pro...

In this article we develop a new approach to construct solutions of stochastic equations with merely measurable drift coefficients. We aim at demonstrating the principles of our technique by analyzing strong solutions of stochastic differential equations driven by Brownian motion.An important and rather surprising consequence of our method which is...

In this paper, we use techniques of Malliavin calculus and forward integration to present a general stochastic maximum principle for anticipating stochastic differential equations driven by a Lévy type of noise. We apply our result to study a general stochastic differential game problem of an insider.

In this paper we employ Malliavin calculus to derive a general stochastic maximum prin-ciple for stochastic partial differential equations with jumps under partial information. We apply this result to solve an optimal harvesting problem in the presence of partial information. Another application pertains to portfolio optimization under partial obse...

In this paper, we introduce Skorohod-semimartingales as an expanded concept of classical semimartingales in the setting of Lévy processes. We show under mild conditions that Skorohod-semimartingales similarly to semimartingales admit a unique decomposition.

In this paper we suggest a general stochastic maximum principle for optimal control of anticipating stochastic differential equations driven by a Lévy-type noise. We use techniques of Malliavin calculus and forward integration. We apply our results to study a general optimal portfolio problem of an insider. In particular, we find conditions on the...

In this paper, we derive the evolution of a stock price from the dynamics of the "best bid" and "best ask". Under the assumption that the bid and ask prices are described by semimartingales, we study the completeness and the possibility for arbitrage on such a market. Further, we discuss (insider) hedging for contingent claims with respect to the s...

In a recent work \cite{BG}, given a collection of continuous semimartingales, authors derive a semimartingale decomposition from the corresponding ranked processes in the case that the ranked processes can meet more than two original processes at the same time. This has led to a more general decomposition of ranked processes. In this paper, we deri...

Given a finite collection of continuous semimartingales, a semimartingale decomposition of the corresponding ranked (order-statistics) processes was derived recently in [11. Banner , A.D. , and Ghomrasni , R. 2008 . Local times of ranked continuous semimartingales . Stochastic Processes and Applications 118 : 1244 – 1253 . View all references]. I...