Published papers

Our goal in this paper is to give a representation of the mean-variance hedging strategy for models whose asset price process is discontinuous as an extension of Gouriéroux, Laurent and Pham (1998) and Rheinländer and Schweizer (1997). However, we have to impose some additional assumptions related to the variance-optimal martingale measure.

We suggest a new valuation method of contingent claims for complete markets. Since our new valuation is closely related to shortfall risk, our suggestion would be useful to study shortfall risk measures which are convex risk measures induced by shortfall risk. We firstly give a brief introduction of shortfall risk measures, and discuss a general form of the valuation. We shall then deal with diffusion type models which are complete market models with underlying assets described by diffusion processes. In particular, the valuation for American type claims is discussed.

We consider, throughout this paper, an incomplete financial market which is governed by a possibly nonlocally bounded right-continuous with left-limits (RCLL) special semimartingale. We shall provide good deal bounds for contingent claims induced by shortfall risk in the framework of the Orlicz heart setting. We prove that the upper and lower bounds of such a good deal bound are expressed by a convex risk measure on an Orlicz heart. In addition, we obtain representation results for three types of model, which are an unconstrained portfolio model, a W-admissible model, and a predictably convex model.

We focus on, throughout this paper, convex risk measures defined on Orlicz spaces. In particular, we investigate basic properties of inf-convolutions defined between a convex risk measure and a convex set, and between two convex risk measures. Moreover, we study shortfall risk measures, which are convex risk measures induced by the shortfall risk. By using results on inf-convolutions, we obtain a robust representation result for shortfall risk measures defined on Orlicz spaces under the assumption that the set of hedging strategies has the sequential compactness in a weak sense. We discuss in addition a construction of an example having the sequential compactness.

We propose, in this paper, a new valuation method for contingent claims, which approximates to the exponential utility indifference valuation. In particular, we treat both ask and bid valuations. In the definition of the exponential utility indifference valuation, we require strong integrability for the underlying contingent claim. The new valuation in this paper succeeds in reducing it by using a kind of power functions instead of the exponential function. Furthermore, we shall investigate some basic properties and an asymptotic behavior of the new valuation.

We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models.

We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai & Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk measure a good deal valuation; and study its properties. We also discuss superhedging cost and Fundamental Theorem of Asset Pricing for convex constrained markets.

We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized by several equivalent properties and in particular, we see that a convex risk measure is a good deal valuation only if it is given as a risk indifference price. An application to shortfall risk measure is given. In addition, we show that the no-free-lunch (NFL) condition is equivalent to the existence of a relevant convex risk measure, which is a good deal valuation. The relevance turns out to be a condition for a good deal valuation to be reasonable. Further, we investigate conditions under which any good deal valuation is relevant.

For the Barndorf-Nielsen and Shephard model, we present approximate expressions of call option prices based on the decomposition formula developed by [T. Arai (2021) Alos type decomposition formula for Barndor-Nielsen and Shephard model, Journal of Stochastic Analysis 2 (2), 3]. Besides, some numerical experiments are also implemented to make sure how effective our approximations are.

We construct a new class of semi-selfsimilar processes as limiting processes of some random walks in random scenery, which extends the class of selfsimilar processes studied by Kesten and Spitzer (1979). © 2001 by the University of Notre Dame. All rights reserved.

Qu, Dassios, and Zhao (2021) suggested an exact simulation method for tempered stable Ornstein-Uhlenbeck processes, but their algorithms contain some errors. This short note aims to correct their algorithms and conduct some numerical experiments.

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 under some boundary conditions 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.

Our purpose is to study properties and representations of convex risk measures for possibly unbounded c adl ag processes. As the underlying space on which we define convex risk measures we consider spaces of cadlag processes whose supremum belongs to an Orlicz heart. In order to obtain concrete representations for such convex risk measures, we shall investigate representations of continuous linear functionals on the underlying space. Moreover, many examples of risk measures are introduced. In particular, we deal with risk measures associated with hedging and pricing problems for American claims. Among others, we look into shortfall risk measure in detail.

The aim of this paper is to give an extension of the mean-variance hedging problem to the L-p-setting, where 1 < p < infinity. Remark that the mean-variance hedging is corresponding to the case where p = 2. Firstly, we prove that the unique existence of the optimal hedging strategy in the L-p-sense, which is the L-p-projection of the underlying contingent claim onto a suitable space of stochastic integrations. Next, we obtain its feedback representation under some additional assumptions. Moreover, the valuation problem induced by the L-p-projections naturally is discussed.