Welcome to my page!
I am Yuki Shigeta, an associate professor at Tokyo Keizai University.
My research field is finance.
Specifically, I am concerned with portfolio theory and asset pricing.
Name: Yuki Shigeta
Position: Associate Professor, Faculty of Economics, Tokyo Keizai University
Degree: Ph.D. in Economics, Kyoto University, September 2016
Research Field: Financial Economics and Mathematical Finance
Date and Place of Birth: April 1988, Japan
Email: sy46744[at]gmail.com
Please replace [at] to @.
There is more information available on research map.
Shigeta, Y., (2025) "An economic interpretation and mathematical analysis of Epstein–Zin stochastic differential utility in infinite horizon when θ<0," Accepted at Finance and Stochastics. [WP ver.](SSRN)
[Abstract] Recent studies highlight the difficulties in infinite-horizon Epstein–Zin stochastic differential utility from economic and mathematical perspectives when the coefficient of relative risk aversion and the elasticity of intertemporal substitution exceed one (i.e., θ<0). We demonstrate that the economically problematic behavior identified in recent studies disappears by an order-equivalent transformation of the utility index. Furthermore, we introduce an admissible set of consumptions to tackle mathematical issues for existence of the utility. For applications, we examine a Merton problem and demonstrate that an optimal control derived from the Hamilton–Jacobi–Bellman equation is admissible and optimal under mild conditions.
Shigeta, Y., (2022) "Quasi-hyperbolic discounting under recursive utility and consumption–investment decisions," Journal of Economic Theory 204, Article Number 105518 . [DOI](Open Access)
[Abstract] This paper examines an Epstein–Zin recursive utility with quasi-hyperbolic discounting in continuous time. I directly define the utility process supporting the Hamilton–Jacobi–Bellman (HJB) equation in the literature and consider Merton's optimal consumption–investment problem for application. I show that a solution to the HJB equation is the value function. The numerical and mathematical analyses show that unlike in the constant relative risk aversion utility, present bias in the Epstein–Zin utility causes economically significant overconsumption, maintaining a plausible attitude toward risks. Additionally, the sophisticated agent's preproperation occurs if and only if the elasticity of intertemporal substitution is larger than one.
Shigeta, Y., (2020) "Gain/loss asymmetric stochastic differential utility," Journal of Economic Dynamics and Control 118, Article Number 103975. [DOI](Open Access)
[Abstract] This study examines a gain/loss asymmetric utility in continuous time in which the investor discounts their utility gain by more than the utility loss. By employing the theory of stochastic differential utility, the model allows an endogenously time-varying subjective discount rate. In addition, the model can express various forms of utility functions including a version of the Epstein–Zin utility. Under the model, even if the state variables do not have any jump in their paths, the optimal consumption/wealth ratio and portfolio weight can change non-smoothly.
Shigeta, Y., (2017) "Portfolio selections under mean-variance preference with multiple priors for means and variances," Annals of Finance 13(1), 97-124. [DOI]
[Abstract] We study portfolio selections under mean-variance preference with multiple priors for means and variances. We introduce two types of multiple priors, the priors for means and the priors for variances of risky asset returns. As our framework, in the absence of a risk-free asset, the global minimum-variance portfolio is optimal when the investor is extremely ambiguity averse with respect to means, and the equally weighted portfolio is optimal when the investor is extremely ambiguity averse with respect to variances.
Shigeta, Y., (2023) "A continuous-time utility maximization problem with borrowing constraints in macroeconomic heterogeneous agent models: A case of regular controls under Markov chain uncertainty," SSRN
[Abstract] This paper is concerned with the verification of a continuous-time utility maximization problem frequently used in recent macroeconomics. By focusing on Markov chain uncertainty, the problem in this paper can feature many characteristics of a typical consumer's problem in macroeconomics, such as borrowing constraints, endogenous labor supply, unhedgeable labor income, multiple asset choice, stochastic changes in preference, and others. I show that the value function of the problem is actually a constrained viscosity solution to the associated Hamilton–Jacobi–Bellman equation. Furthermore, the value function is continuously differentiable in the interior of its domain. Finally, the candidate optimal control is admissible, unique, and actually optimal. (Note: This is an update version of this working paper in Kyoto university )
Shigeta, Y., (2023) "Existence of invariant measure and stationary equilibrium in a continuous-time one-asset Aiyagari model: A case of regular controls under Markov chain uncertainty," SSRN, Presentation Slide
[Abstract] This paper is concerned with the existence of the invariant measure and stationary equilibrium in a continuous-time Aiyagari model with an endogenous labor supply. First, I demonstrate that the value function, optimal consumption, optimal labor supply, optimal saving rate, and optimally controlled liquid asset process are jointly continuous in parameters such as the interest rate and wage. Second, I show the existence of the ergodic invariant measure of the optimally controlled liquid asset process. Finally, I demonstrate the existence of the stationary equilibrium in a continuous-time one-asset Aiyagari model. (Note: This is an update version of this working paper in Kyoto university )
This page is still a work in progress. Sorry.