[00879] Stochastic analysis in mathematical finance
Session Time & Room : 4E (Aug.24, 17:40-19:20) @F412
Type : Proposal of Minisymposium
Abstract : In this minisymposium the recent advances in mathematical finance will be discussed. The topics include stochastic analysis of jump processes, stochastic optimization, partial differential equations, stochastic calculus of variations, and mathematical aspects of data science for pricing and hedging of financial products. This minisymposium will bring together researchers with the aim to stimulate discussions for both theoretical and practical advancement.
Organizer(s) : Takuji Arai, Tomoyuki Ichiba
Sponsor : This session is sponsored by the SIAM Activity Group on Financial Mathematics and Engineering.
[03804] Constrained optimal stopping under a regime-switching model
Format : Talk at Waseda University
Author(s) :
Takuji Arai (Keio University)
Abstract : We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a specific regime. The main objectives are to show that an optimal stopping time exists as a threshold type and to derive expressions of the value functions and the optimal threshold. To this end, we solve the corresponding variational inequality and show that its solution coincides with the value functions. Some numerical results are also introduced. Furthermore, we investigate some asymptotic behaviors.
[04565] Remarks on pathwise Itô calculus in infinite dimensions
Format : Talk at Waseda University
Author(s) :
Yuki Hirai (National Institute of Technology, Tsuruoka College)
Abstract : The Itô–Föllmer calculus, pioneered by Föllmer (1981), is a deterministic counterpart to classical Itô's stochastic calculus. It has recently been receiving increasing attention from the viewpoint of its financial applications. In this talk, we extend some results in the Itô–Föllmer calculus to infinite dimensional settings.
[03809] Systemic Risk and Overconfidence under Stochastic Environment
Format : Talk at Waseda University
Author(s) :
Li-Hsien Sun (National Central University)
Abstract : We propose an optimal portfolio problem based on the mean variance criterion based on the relative performance with the feature of overconfidence. Namely, investors intend to maximize the distance between the average and minimize the their own variance as well. In the meantime, they also consider the better return than the real one due to overconfidence. We illustrate systemic risk by applying the probability of the large number of defaults. Finally, the influence of overconfidence is discussed through numerical analysis.
[03808] Smoothness of Directed Chain Stochastic Differential Equations and Its Applications
Format : Talk at Waseda University
Author(s) :
Tomoyuki Ichiba (University of California Santa Barbara )
Abstract : On a filtered probability space for the space of continuous functions, we shall consider a system of stochastic equations called directed chain stochastic differential equations for a pair of stochastic processes whose marginal distributions in the path space are identical and their joint distribution is uniquely determined by the system of equations with the distributional constraints. In this talk we discuss the smoothness of the solutions of the equations under some regular conditions and introduce its applications of such systems to the stochastic filtering problem and to the generative adversarial network problem in finance.
