This paper proposes a new hedging scheme of European derivatives under uncertain volatility environments, in which a weighted variance swap called the polynomial variance swap is added to the Black-Scholes delta hedging for managing exposure to volatility risk. In general, under these...

This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in best approximation in an inner product space. Moreover, we applies “Dykstra's cyclic projections algorithm” for its implementation. Numerical examples...

This article presents an equilibrium-based multi-agent optimal consumption and portfolio problem incorporating sentiments, where multiple agents have heterogeneous (optimistic, pessimistic, neutral) views on fundamental risks represented by Brownian motions.Each agent maximizes its expected...