An optimal consumption and investment problem with partial information

We consider a finite-time optimal consumption problem where an investor wants to maximize the expected hyperbolic absolute risk aversion utility of consumption and terminal wealth. We treat a stochastic factor model in which the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case in which the investor cannot observe the factor process and uses only past information of risky assets. Then our problem is formulated as a stochastic control problem with partial information. We derive the Hamilton–Jacobi–Bellman equation. We solve this equation to obtain an explicit form of the value function and the optimal strategy for this problem. Moreover, we also introduce the results obtained by the martingale method.

A maximum principle for controlled stochastic factor model

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 differential equation (SPDE). We then give a sufficient maximum principle for a system of controlled SDEs and degenerate SPDE. We also derive an equivalent stochastic maximum principle. We apply the obtained results to study a pricing and hedging problem of a commodity derivative at a given location, when the convenience yield is not observable.

A GENERAL OPTIMAL INVESTMENT MODEL IN THE PRESENCE OF BACKGROUND RISK

In this paper we present two dynamic models of background risk. We first present a stochastic factor model with an additive background risk. Then, we present a dynamic model of simultaneous (correlated) multiplicative background risk and additive background risk. In so doing, we use a general utility function.

THE INTERACTION BETWEEN THE FINANCIAL SECTOR AND THE REAL SECTOR: A STOCHASTIC MODEL

Using a stochastic factor model, we devise a method to estimate the marginal impact of real GDP on the stock market. We apply our approach to the Jamaican financial market.