Research

Research Fields

These are the fields recorded in the Tokyo University of Science researcher database. My JSPS KAKENHI project is reviewed under Basic Section 60020, Mathematical informatics-related.

Overview

I work on numerical analysis for continuous-time stochastic optimal control, and on its applications to mathematical finance.

The control problems I study lead to Hamilton–Jacobi–Bellman equations and, when the control is combined with impulse-type decisions, to quasi-variational inequalities. These partial differential equations rarely admit explicit solutions once realistic constraints are imposed, so I develop and analyse numerical schemes for them — implicit methods for finite time horizons, and collocation methods built on twice integrated kernels and radial basis function interpolation.

The applications are portfolio optimization problems that cannot be solved in closed form: management under no-short-selling and leverage constraints, liability tracking for pension funds, optimal execution under stochastic price recovery, and portfolio selection under downside risk measures such as expected shortfall.

Research Theme

Publications and Talks