Ricardo Josa-Fombellida

• University of Valladolid

We study the time-consistent investment and contribution policies in a defined benefit stochastic pension fund where the manager discounts the instantaneous utility over a finite planning horizon and the final function at constant but different instantaneous rates of time preference. This difference, which can be motivated for some uncertainties af...

We consider the time consistent management of a defined benefit stochastic pension plan where the participants have different rates of time preference and the fund manager collects this heterogeneity when discounting the future. The main objective is to select the amortization rate and the investment strategy minimizing both the contribution rate r...

This paper aims to characterize a class of stochastic differential games, which satisfy the certainty equivalence principle beyond the cases with quadratic, linear, or logarithmic value functions. We focus on scalar games with linear dynamics in the players' strategies and with separable payoff functionals. Our results are based on the resolution o...

We study the optimal management of an aggregated overfunded pension plan of defined benefit type as a two-player noncooperative differential game. The model's key fact is to consider the fund surplus as a strategic variable that makes the pension plan more attractive both for current and future participants. We let the worker participants to act co...

The paper studies the optimal asset allocation problem of a defined benefit pension plan that operates in a financial market composed of risky assets whose prices are constant elasticity variance processes. The benefits paid to the participants are deterministic. The contributions to the fund are designed by a spread amortization method, which take...

It is generally admitted that a correct forecasting of uncertain variables needs Markov decision rules. In a dynamic game environment, this belief is reinforced if one focuses on credible actions of the players. Usually, subgame perfectness requires equilibrium strategies to be constructed on Markov rules. It comes as a surprise that there are inte...

This paper analyzes a noncooperative and symmetric dynamic game where players have free access to a productive asset whose evolution is a diffusion process with Brownian uncertainty. A Euler-Lagrange equation is found and used to provide necessary and sufficient conditions for the existence and uniqueness of a smooth Markov Perfect Nash Equilibrium...

We study the asset allocation of defined benefit pension plans of the type designed and sponsored by firms with the aim of providing a lifetime pension to the employees at the age of retirement. Benefits are stochastic, combining Poisson jumps with Brownian uncertainty. The sponsor dynamically forms portfolios where the risky asset is also subjecte...

The paper provides a systematic way for finding a partial differential equation that directly characterizes the optimal control, in the framework of one-dimensional stochastic control problems of Mayer type, with no constraints on the controls. The results obtained are applied to continuous-time portfolio problems.

In this paper we study the optimal management of an aggregated pension fund of defined benefit type, in the presence of a stochastic interest rate. We suppose that the sponsor can invest in a savings account, in a risky stock and in a bond with the aim of minimizing deviations of the unfunded actuarial liability from zero along a finite time horizo...

In this paper we study the problem of simultaneous minimization of risks, and maximization of the terminal value of expected funds assets in a stochastic defined benefit aggregated pension plan. The risks considered are the solvency risk, measured as the variance of the terminal fund’s level, and the contribution risk, in the form of a running cost...

In this paper we consider the optimal management of an aggregated dynamic pension fund. There are n classes of workers whose salaries are stochastic. A portion of the salary is contributed to the funding process and the manager invests in a portfolio with m risky assets and a risk-free security. The main objective is to minimize the cost of contrib...

This paper provides new insights into the solution of optimal stochastic control problems by means of a system of partial differential equations, which characterize directly the optimal control. This new system is obtained by the application of the stochastic maximum principle at every initial condition, assuming that the optimal controls are smoot...

The question we address is the optimal management of an aggregated pension fund ofde¯ned bene¯t type, in the presence of a stochastic interest rate. The sponsor can investin a savings account, stocks and a bond with the following aim: to minimize deviations ofterminal unfunded actuarial liability from zero. We solve the problem by means of optimals...

In this paper the optimal management of an aggregated dynamic pension fund is studied. To cover the promised liabilities to workers at the age of retirement, the plan sponsor continuously manages time-varying funds. He or she can choose the rate of contribution to the fund, the investment in a given number of risky assets, and a security with const...

This paper provides new insights into the solution of optimal stochastic control problems by means of a system of partial differential equations, which characterize directly the optimal control. This new system is obtained by the application of the stochastic maximum principle at every initial condition, assuming that the optimal controls are smoot...

We consider a continuous time dynamic pension funding model in a defined benefit plan of an employment system. The benefits liabilities are random, given by a geometric Brownian process. Three different situations are studied regarding the investment decisions taken by the sponsoring employer: in the first, the fund is invested at a constant, risk-...

The tradeoff between risk and return in equity markets is well established. This paper examines the existence of the same tradeoff in the single-family housing market. For home buyers, who constitute about two-thirds of U.S. households, the choice about how much housing and which house to buy is a joint consumption/investment decision. Does this co...

El enfoque clásico para el estudio de pro lemas de control estocástico se asa en la ecuación de Hamilton-Jacobi-Bellman, que caracteriza a la función valor óptimo En este trabajo mostramos que en ciertos problemas es posible deducir ecuaciones en derivadas parciales que caracterizan directamente al control óptimo y que presentan una estructura más...

Se considera un plan de pensiones en el que el gestor invierte en dos activos, uno con riesgo y otro sin riesgo, al tiempo que determina el tanto de contribución de forma que se minimicen los riesgos de contribución y de solvencia, en un horizonte temporal no acotado. Se impone la condición de que no hay posibilidad de venta del activo con riesgo....

The paper provides a systematic way for finding a partial differential equation that characterize directly the optimal control, in the framework of one�dimensional stochastic control problems of Mayer, with no constraints on the controls. The results obtained are applied to some significative models in financial economics.

This paper gives a new method to characterize Markov Perfect Nash Equilibrium in stochastic differential games by means of a set of Generalized Euler Equations. Necessary and sufficient conditions are given.

El proyecto se realiza en la Facultad de Ciencias Económicas y Empresariales de la Universidad de Valladolid. Los profesores implicados en el proyecto son dos. El objetivo es doble, por una parte poner en marcha y consolidar la asignatura 'Informática aplicada a la Economía' y por otra, crear su metodología docente. El sistema de trabajo ha consist...