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.
This paper extends the optimal investment control framework by incorporating fractional Brownian motion to capture long-range dependence and memory effects in asset prices. Replacing the standard Brownian component with a fractional Brownian motion governed by the Hurst parameter H with H∈(1/2,1), we employ the Wick–It...
We study a representative-agent Epstein-Zin economy with geometric dividends and a hidden finite-state Markov drift. We allow the price-dividend ratio to contain an additional positive, absolutely continuous valuation factor and, within the class $\mathfrak C$ defined below and under the regularity, admissibility, and...
We develop a market-informed valuation framework for guaranteed minimum maturity benefit (GMMB) riders with rational surrender under the Heston stochastic-local volatility (SLV) model. The guarantee is written on the fee-deducted account value and is considered both in its terminal-only form and in the presence of earl...
Ludovic Goudenège, Andrea Molent, Xiao Wei et al.· 0 citations
We develop a PDE-based methodology for pricing and hedging European contingent claims in general one-dimensional diffusion markets characterized solely by their scale function and speed measure, possibly without a classical SDE representation, and with constant interest rate. We derive a hedging equation whose solution...
Alexis Anagnostakis, D. Criens, M. Urusov· 0 citations
This paper develops a stylized continuous-time framework for open-end fund investment in which state-dependent fund flows, passive benchmarking, and strategic manager–investor interaction are modeled jointly. The contribution is not a new Stackelberg solution concept; rather, it is the economic mechanism created by com...
Yin Li, Ya-Zhi Song, Can Zhou et al.· Mathematics· 0 citations
