This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate...

This paper presents an application of a linear quadratic stochastic differential game to a financial model that describes trading behaviors of different types of players in a high frequency stock market. Stability of the stock market in a high frequency environment is a central issue in...

This paper considers a multi-agent optimal investment problem with conservative sentiments in an incomplete market by a BSDE approach. Particularly, we formulate the conservative sentiments of the agents by a sup-inf/inf-sup problem where we take infimum on a choice of a probability measure and...