Optimal Merton's Problem under Multivariate Affine Volterra Models with Jumps
How investors should rebalance portfolios when markets jump unpredictably
Investors often adjust their portfolios based on past market patterns, but real markets jump suddenly and have memory — past prices influence future ones in ways classical models ignore. This paper solves the classic portfolio-balancing problem for these more realistic, jumpy markets with memory, deriving concrete investment strategies that account for both kinds of market friction.
Standard portfolio advice assumes smooth, memoryless markets — assumptions that fail during crashes and volatility clusters. This work provides investors and fund managers with mathematically rigorous strategies tailored to real market behavior, potentially improving returns and risk management when applied to multi-asset portfolios.