Utility Indifference Valuation for Defaultable Claims under a Structural Model with Hawkes Jump-Diffusion Processes

We study the utility indifference valuation of defaultable contingent claims in a Black–Cox structural framework where the firm’s asset value follows a Hawkes-type jump-diffusion process. The self-exciting and path-dependent jump intensity captures clustering effects of shocks and allows for self-contagion in the firm’s asset dynamics. The valuation problem is formulated as a stochastic control problem. By applying the dynamic programming principle, we derive a nonlinear second-order partial integro-differential equation that characterizes the value function. A Feynman–Kac type representation is then employed to construct a candidate solution and analyze the associated nonlinear operator in a suitable functional space, which enables us to establish the existence and uniqueness of the solution. Based on the obtained representation, we derive the corresponding utility indifference prices for defaultable bonds and credit default swaps. Numerical experiments illustrate the effects of key model parameters on the indifference prices.