Portfolio Optimization Problems

Project Details


We propose a optimal portfolio problem where the underlying is driven by the factor model with delay feature in order to describe the interaction with time delay among different financial markets. The delay phenomenon can be recognized as the integral type and the pointwise type. Due to the delay leading to the non-Markovian structure, we obtain the optimal strategy through the coupled forward and backward stochastic differential equations (FBSDEs). The existence and uniqueness of the coupled FBSDEs are also studied. We analyze three particular cases where the corresponding FBSDEs can be solved explicitly. In addition, we consider the problem of optimal investment by an insurer where the claim size is driven by Brownian motion. The optimal strategy is obtained using the coupled FBSDEs. Finally, we analyze the model of high frequency trading in order to obtain the optimal ask quote based on the feature observed in financial markets under relative performance. The Nash equilibria are solved using the coupled Hamilton Jacobi Bellman (HJB) equations.
Effective start/end date1/08/1831/07/19

UN Sustainable Development Goals

In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):

  • SDG 12 - Responsible Consumption and Production
  • SDG 13 - Climate Action
  • SDG 17 - Partnerships for the Goals


  • Delay factor model
  • optimization
  • coupled forward and backward stochastic differential equations
  • high frequency trading
  • stochastic differential games
  • relative performance
  • Nash equilibrium


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