Abstract In quantitative finance, there have been numerous new aspects and developments related with the stochastic control optimization problems which handle controlled variables of performing behavior a dynamical system to achieve certain objectives. this paper, we address optimal trading strategies via price impact models using Heston volatility framework including jump processes either in o...

This paper investigates the limit behavior of Markov decision processes (MDPs) made of independent particles evolving in a common environment, when the number of particles goes to infinity. In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal co...

We develop a unifying approach for approximating a “limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or “almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to stat...

In this work we ask how should an investor distribute wealth over various assets to maximizethe growth rate of the cumulative wealth in a discrete time market with proportional transactioncosts. We show that this sequential decision problem has a stationary optimal policy. Inaddition, we show that for all 2 > 0 there exists a policy that guarantees a growth rate at most 2bel...

In this paper, we focus on the optimal software testing/maintenance problem considered in Rinsaka and Dohi (2004), and develop a stochastic model in discrete operation circumstance, under the difference between the software testing environment and the operational environment can be characterized by an environment parameter. More precisely, the total expected software cost is formulated via the ...

We develop a unifying approach for approximating a \limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or \almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to stat...