MDP algorithms for portfolio optimization problems in pure jump markets
The authors consider the classical problem of maximizing the expected utility of the terminal wealth of a portfolio in a financial market with general utility function. A continuous-time pure jump market is considered. It is assumed that jumps in the stock prices arrive in accordance with a Poisson process and that the relative jumps heights of the stocks are independent and identically distributed random vectors. The behavior of the stock prices between jumps is purely deterministic. Thus, the price processes fall in the class of piece-wise deterministic Markov processes. With the help of an embedding procedure, the optimal control problem is solved by looking at a discrete-time contracting Markov decision process. It is proved that the value function is the unique fixed point of a dynamic programming operator and that the value iteration as well as the policy iteration holds. The existence of an optimal stationary portfolio is established.
piecewise deterministic Markov processes
scientific article; zbMATH DE number 5697477
scientific article