One-day workshop on stochastic control, finance, and related issues 



開催日時: 2024年7月4日(木曜)

Date: July 4 (Thu), 2024

会場 : 大阪大学豊中キャンパス基礎工学国際棟 アクセス

Venue : Engineering Science International Hall, Toyonaka campus, Osaka University Access


プログラム / Program：

タイトル / Title

Bridges

概要 / Abstract

A shared interest for the theory and applications of stochastic bridges laid lasting foundations for joint research and academic endeavours with Professor Jun Sekine, while building a strong bridge to Japan. In this presentation, we shall explore how randomized Markov bridges took shape and have led to new ideas and applications of information-based asset pricing. Meantime, stochastic bridges have become arcades, a new class of interpolating stochastic processes with an intriguing connection to stochastic optimal transport. And where it was a first bridge, so too has the engagement with Japanese academics grown to become knowledge arcades linking more researchers at their universities and institutes in Japan and abroad.  


タイトル / Title

Expected exponential utility maximization problem with a nonlinear factor model and its policy improvement algorithm

概要 / Abstract

 In this talk, we propose a policy improvement algorithm for an optimal investment problem to maximize an expected exponential utility of terminal wealth. We employ a general stochastic factor model where the returns and volatilities of assets are random and affected by some economic factors, modeled as diffusion processes. We establish an iteration procedure that converges to the value function and the optimal strategies.


タイトル / Title

Multi-stage Euler-Maruyama methods for backward stochastic differential equations driven by continuous-time Markov chains

概要 / Abstract

We study numerical methods for computing the solutions of Markov backward stochastic differential equations (BSDEs) driven by continuous-time Markov chains (CTMCs). In this talk, we present our main contributions as follows: (1) We observe that Euler-Maruyama temporal discretization methods for solving Markov BSDEs driven by CTMCs are equivalent to exponential integrators for solving the associated systems of ordinary differential equations (ODEs). (2) We introduce multi-stage Euler-Maruyama methods for effectively solving “stiff” Markov BSDEs driven by CTMCs; these BSDEs typically arise from the spatial discretization of Markov BSDEs driven by Brownian motion; (3) We propose a multilevel spatial discretization method on sparse grids that efficiently approximates high-dimensional Markov BSDEs driven by Brownian motion with a combination of multiple Markov BSDEs driven by CTMCs on grids with different resolutions. This talk is based on a PhD thesis under the supervision of Professor Jun Sekine. 


タイトル / Title

Dynamics of First-to-Default Swap in an Information Flow-Based Approach (joint work with Hideyuki Takada)

概要 / Abstract

We study the impact of default contagion risk on the prices of defaultable bonds and credit derivatives with an information flow-based credit risk model pioneered by Brody, Hughston, and Macrina (2010). In our previous work, Nakagawa and Takada (2023),  we derive the stochastic differential equations (SDEs) satisfied by a pair of discounted bond price processes and make apparent some characteristics of the price dynamics in terms of continuous and jump martingales. In this talk, we first introduce our information flow-based credit risk model and then show the SDEs for the FtD spread to argue some dynamic characteristics of the FtD spread.


タイトル / Title

Optimal Risk Sharing Problem with Constraints - An application of Double Barrier BSDE  

概要 / Abstract

Optimal risk sharing problem (ORSP) has become classical topics in economics, insurance and finance.  In the insurance context, agent A plays a role of an insured who is interested in having an insurance protection  against claims, and agent B plays the role of an insurer. In that, we could recognize that ORSP is a problem  between the two parties who value their future risky positions with dynamic risk measures, which are closely  related to Backward Stochastic Differential Equation (BSDE).  Also, as we are interested in Double Barrier BSDE  (DBBSDE) as an  application of BSDEs, we are tackling “Optimal risk sharing problem with constraints”, by combining  DBBSDE and ORSP.


タイトル / Title

Policy gradient learning methods for stochastic control with exit time and applications to share repurchase pricing 

概要 / Abstract

We develop policy gradients methods for stochastic control with exit time in a model-free setting. We propose two types of algorithms for learning either directly the optimal policy or by learning alternately the value function (critic) and the optimal control (actor).  The use of randomized policies is crucial for overcoming notably the issue related to the exit time in the gradient computation. We demonstrate the effectiveness of our approach by implementing our numerical schemes in  the application to the problem of share repurchase pricing. Our results show that the proposed policy gradient methods  outperform PDE or other neural networks techniques in a model-based setting. Furthermore, our algorithms are flexible enough to incorporate realistic market conditions like e.g.  price impact or transaction costs. Based on joint work with M. Hamdouche and P. Henry-Labordère


タイトル / Title

Notes on LDC and RMB

概要 / Abstract

Problems I worked on before are revisited: That is, 1) Large Deviations Control, which originated from Pham (2003), and 2) Randomized Markov Bridges, which are called "information processes" and utilized in stochastic financial modeling in the original work, Brody, Hughston, and Macrina (2008). Concerning these problems, some (partial) results and related (open) questions will be provided and mentioned.



懇親会 / Party : がんこ石橋

懇親会参加登録 / Registration: https://forms.gle/r1ZwRrAZZbqCxa4w6 (参加登録締め切り: 6月17日 (月))


世話人：

深澤正彰（大阪大学），濱口雄史（京都大学），畑宏明（一橋大学），平井祐紀（鶴岡工業高等専門学校），安田和弘（法政大学）

Organizers：

Masaaki Fukasawa (Osaka University), Yushi Hamaguchi (Kyoto University), Hiroaki Hata (Hitotsubashi University), Yuki Hirai (National Institute of Technology, Tsuruoka College), Kazuhiro Yasuda (Hosei University)