Chonghu Guan

• Lecturer at Jiaying University

This paper is concerned with a long standing optimal dividend payout problem in insurance subject to the so-called ratcheting constraint, that is, the dividend payout rate shall be non-decreasing over time. The surplus process is modeled by a drifted Brownian motion process and the aim is to find the optimal dividend ratcheting strategy to maximize...

We study Markowitz’s mean-variance portfolio selection problem in a continuous-time Black–Scholes market with different borrowing and saving rates. The associated Hamilton–Jacobi–Bellman equation is fully nonlinear. Using a delicate partial differential equation and verification argument, the value function is proven to be C3,2\documentclass[12pt]{...

In this paper, we discuss an optimal dividend and reinsurance problem for an insurance company facing two types of risks: unstable income and potential loses. The arrival of all loses is characterized as a compound Poisson process. We assumes that every possible loss can be reinsured for a part of it. The reserve is a combination of a diffusion pro...

In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock whose price is driven by unobservable market status and noise processes. The free boundary problem is a variational inequality system of three functions with a degenerate operator. We prove that all the four switching free boundaries are no-over...

This paper studies a life-time consumption-investment problem under the Black-Scholes framework, where the consumption rate is subject to a lower bound constraint that linearly depends on the investor's wealth. It is a stochastic control problem with state-dependent control constraint to which the standard stochastic control theory cannot be direct...

This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurance company in a finite time horizon. The goal of the company is to maximize the expected cumulative discounted dividend payouts until bankruptcy or maturity, whichever comes earlier. The company is allowed to buy reinsurance contracts dynamically over the who...

This paper investigates a continuous-time mean-variance hedging problem under different loan and deposit rates. The value function is shown to satisfy a fully nonlinear PDE and be of $C^{3,2}$ smooth by PDE method and verification theorem. We show that there are a borrowing and a saving boundary that divide the whole trading space into three region...

This paper considers a life-time consumption-investment problem under the Black-Scholes framework, where the investor's consumption rate is subject to a lower bound constraint that linearly depends on the investor's wealth. Due to the state-dependent control constraint, the standard stochastic control theory cannot be directly applied to our proble...

This paper considers an optimal investment problem under CRRA utility with a borrowing constraint. We formulate it into a free boundary problem consisting of a fully nonlinear equation and a linear equation. We prove the existence and uniqueness of the classical solution and present the condition for the existence of the free boundary under a linea...

In this paper, we consider the problem of how to run an insurance company to minimize the ruin probability in a finite time horizon. The value function v with the corresponding optimal reinsure strategy a∗ is the solution of the following fully nonlinear equation vt−12σ02vxx+γvx−inf0≤a≤1(12σ2a2vxx+μavx)=0under initial–boundary condition v(0,t)=1, v...

In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock that is driven by a uncertain market status process. The free boundary problem is a variational inequality system of three functions with a degenerate operator. The main contribution of this paper is that we not only prove all the four switching...

This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurer in a finite time horizon. The goal of the insurer is to maximize its expected cumulative discounted dividend payouts until bankruptcy or maturity which comes earlier. The insurer is allowed to dynamically choose reinsurance contracts over the whole time hori...

This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in [0,M] and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The ob...

We develop famous Merton's financial model to more realistic and interesting situation: consumption rate has lower and upper constraints. The aim is to find optimal strategies for consumption and investment. The corresponding HJB equation is a fully nonlinear ordinary differential equation. We use stochastic analysis and differential equation techn...

In this paper, we investigate an optimal stopping problem (mixed with stochastic controls) for a manager whose utility is nonsmooth and noncon-cave over a finite time horizon. The paper aims to develop a new methodology, which is different from those of mixed dynamic optimal control and stopping problems in the existing literature, so as to figure...

We consider a Barenblatt parabolic equationvt−sup0≤a≤1⁡{12a2σ2vxx+aμvx−cv+x}=0. This equation comes from finance. In our model, the risk of the insurance company is controllable. The so-called proportional reinsurance means that it is possible for the cedent to divert 1−a fraction of all premiums to the reinsurance company with the obligation from...

In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a \textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, to figure...

We consider a Barenblatt parabolic equation Arising from a financial stochastic optimal control model. In this model, the control variable l, which is bounded and lies in [0, M], should be chosen to optimize the objective function to take the maximum value. From the problem, it can be seen that l should be either 0 or M, which depends on whether vx...

This article aims to characterize behaviors of the free boundary arising from American butterfly option pricing. We prove the existence and uniqueness of the solution and free boundary. And then, we classify the shape of the free boundary under different conditions. The main contribution of this paper is to prove that the free boundary of evolution...