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This paper aims to explore the relationship between maximum principle anddynamic programming principle for stochastic recursive control problem withrandom coefficients. Under certain regular conditions for the coefficients, therelationship between the Hamilton system with random coefficients andstochastic Hamilton-Jacobi-Bellman equation is obtained. It is very differentfrom the deterministic coefficients case since stochasticHamilton-Jacobi-Bellman equation is a backward stochastic partial differentialequation with solution being a pair of random fields rather than adeterministic function. A linear quadratic recursive utility optimizationproblem is given as an explicitly illustrated example based on this kind ofrelationship.

The Relationship between Maximum Principle and Dynamic Programming Principle for Stochastic Recursive Control Problem with Random Coefficients