arXiv subjects

Yukihiro Tsuzuki

Publications and source records attributed to Yukihiro Tsuzuki.

3 recordsLinked to original sources

arXiv2026

Contingent Claim Valuation under Increasing Profit, Strong Arbitrage, and Arbitrage of the First Kind

We study the upper hedging price for contingent claims in market models with strong types of arbitrage: increasing profit, strong arbitrage, and arbitrage of the first kind. The existence of arbitrage may make the price smaller than if it did not exist. For example, when the asset price process has a reflecting boundary, which introduces increasing profit in the market model, the option prices are reduced to those of the corresponding options that knock-out at the boundary. Furthermore, we demonstrate that corporate stock price processes with increasing profit are obtained as a result of corporate stock issuance and repurchase plans.

q-fin.MF↗

arXiv2025

Pitman's Theorem, Black-Scholes Equation, and Derivative Pricing for Fundraisers

We propose a financial market model that comprises a savings account and a stock. The stock price process is modeled as a one-dimensional diffusion, in which two types of agents exist: an ordinary investor and a fundraiser who buys or sells stocks as funding activities. Although the investor information is the natural filtration of the diffusion, the fundraiser possesses additional information regarding the funding, as well as additional cash flows as a result of the funding. This concept is modeled using Pitman's theorem for the three-dimensional Bessel process. Two contributions are presented: First, the prices of European options for the fundraiser are derived. Second, a numerical scheme for call option prices in a market with a bubble is proposed, where multiple solutions exist for the Black--Scholes equation and the derivative prices are characterized as the smallest nonnegative supersolution. More precisely, the call option price in such a market is approximated from below by the prices for the fundraiser. This scheme overcomes the difficulty that stems from the discrepancy that the payoff shows linear growth, whereas the price function shows strictly sublinear growth.

q-fin.MF↗

arXiv2025

Boundary conditions at infinity for Black-Scholes equations

We propose a numerical procedure for computing the prices of European options, in which the underlying asset price is a Markovian strict local martingale. If the underlying process is a strict local martingale and the payoff is of linear growth, multiple solutions exist for the corresponding Black-Scholes equations. When numerical schemes such as finite difference methods are applied, a boundary condition at infinity must be specified, which determines a solution among the candidates. The minimal solution, which is considered as the derivative price, is obtained by our boundary condition. The stability of our procedure is supported by the fact that our numerical solution satisfies a discrete maximum principle. In addition, its accuracy is demonstrated through numerical experiments in comparison with the methods proposed in the literature.

q-fin.MF↗