Abstract

This talk concerns Nash equilibria in portfolio games with finite and infinite populations, where common noise dynamics are described by integer-valued random measures (e.g., Poisson random measures) in addition to Brownian motions. Within this framework, we analyze optimal investment and hedging under relative performance concerns with exponential (CARA) preferences. We characterize mean-field equilibria via McKean-Vlasov backward SDEs with jumps and prove existence and uniqueness. A key contribution is a structural decomposition of the mean-field equilibrium strategy into investment, hedging, and interaction components. Based on this decomposition, numerical computations illustrate the impact of common noise on the mean-field equilibrium strategies in a Markovian framework using PDE methods. Moreover, building on this decomposition, we show how a new mean-field game of quadratic hedging with relative performance concerns emerges as risk aversion vanishes (i.e., as risk tolerance tends to infinity), without imposing a Markovian restriction.

Joint work with Dirk Becherer; partially based on arXiv:2408.01175.

Seminars in Probability and Finance