Jun Sekine

Solving long term optimal investment problems with Cox-Ingersoll-Ross interest rates

A large deviations control problem is treated for a long term optimal investment on a financial market with a bank account and a risky stock, both of which are affected by a stochastic factor described as Cox-Ingersoll-Ross’s interest rates. The solution is presented in explicit form by investigating the effective domain of the associated risk-sensitive control problem in risk-seeking case.

Long-Term Optimal Investment with a Generalized Drawdown Constraint

The long-term risk-sensitive optimal investment problem is studied with a generalized, nonlinear drawdown constraint. The optimal solution is constructed, using the solution to the baseline optimization problem without drawdown constraint. For the analysis, it is helpful to utilize the properties of the Azema--Yor processes associated with self-financing wealth processes. As a variant, long-term risk-sensitive optimal investment with both drawdown and floor constraints is also considered.

Long-term optimal portfolios with floor

Long-term risk-sensitive portfolio optimization is studied with floor constraint. A simple rule to characterize its solution is mentioned under a general setting. Following this rule, optimal portfolios are constructed in several ways, using the optimal portfolio without floor constraint, combined with ideas of dynamic portfolio insurance, such as CPPI (constant proportion portfolio insurance), OBPI (option-based portfolio insurance), and DFP (dynamic fund protection). In addition, examples are presented with explicit computations of solutions.

Order estimates for the exact Lugannani–Rice expansion

The Lugannani–Rice formula is a saddlepoint approximation method for estimating the tail probability distribution function, which was originally studied for the sum of independent identically distributed random variables. Because of its tractability, the formula is now widely used in practical financial engineering as an approximation formula for the distribution of a (single) random variable. In this paper, the Lugannani–Rice approximation formula is derived for a general, parametrized sequence

Optimal portfolio for a highly risk-averse investor: A differential game interpretation

(X^{(\varepsilon )})_{\varepsilon >0}

On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations

(X(ε))ε>0 of random variables and the order estimates (as

Risk-Sensitive Asset Management under a Wishart Autoregressive Factor Model

\varepsilon \rightarrow 0