Optimal dealer's pricing strategy under regime switching economy

The research examines the optimal behaviour of a single dealer who is faced with a stochastic demand and supply to trade. Their market activities are depicted as the stochastic generation of market orders according to a Markovian Regime Switching Poisson process. The intensities of Bid and Ask orders are assumed to be dependent on the state of the economy and the objective is to effectively describe the temporal microstructure, or moment-to-moment trading activities in asset markets. Using stochastic dynamic programming, we derive the optimal bid and ask prices that maximize the dealer's expected utility of terminal wealth as a function of the state in which they find themself. The relationship of the bid and ask prices to inventory of the dealer, instantaneous variance of return, stochastic arrival of transactions and other variables is examined. Finally, we solve the optimization problem numerically, using a Finite Element Method.