2022/09/10 by Garima Agrawal, Agrawal, Garima, Anindya Goswami +1
Decision Sciences · Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Game Theory and Applications #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2209.04620
openalex publication_date 2022/09/10 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
We model the stock price dynamics through a semi-Markov process obtained using a Poisson random measure. We establish the existence and uniqueness of the classical solution of a non-homogeneous terminal value problem and we show that the expected value of stock price at horizon can be obtained as a classical solution of a linear partial differential equation that is a special case of the terminal value problem studied in this paper. We further analyze the market making problem using the point of view of an agent who posts the limit orders at the best price available. We use the dynamic programming principle to obtain a HJB equation. In no-risk aversion case, we obtain the value function as a classical solution of a linear pde and derive the expressions for optimal controls by solving the HJB equation.