What is the natural scale for a Levy process in modelling term structure of interest rates? (with T.Tsuchiya) arXiv math.PR/0612341[December 2006] This paper gives examples of explicit arbitrage-free term structure models with L\'evy jumps via state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a L\'evy process is a "natural" scale for the process to be the state variable of a market.

Stochastic equation on compact groups in discrete negative time (with C. Uenishi and K. Yano) arXiv matth.PR/0603113 [March 2006] In this paper a stochastic equation on compact groups in discrete negative time is studied. This is closely related to Tsirelson's stochastic differential equation, of which any solution is non-strong. How the group action reflects on　the set of solutions is investigated. It is applied to generalize Yor's result and give a necessary and sufficient condition for existence of a strong solution and for uniqueness in law.

Discrete Ito Formulas and Their Applications to Stochastic Numerics arXiv matth.PR/0603341; appearing in RIMS kokyuroku 1462 202-210 (2006) ; proceedings of the 7th Workshop on Stochastic Numerics; Jun 27--29, 2005, RIMS, Kyoto.[This version November 2005] This is a survey of the author's observations on the discrete-time analogues of It\^o formulas.

Some Remarks on the Inui-Kijima-Ritchken-Sankarasubramanian Model Presented at 2004 Daiwa International Workshop on Financial Engineering, August 2004 In this short note, a new Markovian implementation scheme for the Inui-Kijima- Ritchken-Sankarasubramanian model is introduced..

Lifting Quadratic Term Structure Models to Infinite Dimension (with K. Hara), October 2004, Revised April, 2005 We will introduce an infinite dimensional generalization of quadratic term structure models of interest rates, aiming that the lift will give us a deeper understanding of the classical models. We will show that it preserves some of the favorable properties of the classical quadratic models.

A short report on an extension of Chamberlin's experimental economies. February 2004 In this short paper, first introduced is a multi-goods extension of Chamberlin's experimental economies and then a design of experimental markets is presented. As a proof of the potentiality of our design, some results of experiments are also reported, where interesting natures of the convergence to the equilibria are observed.

Generalizations of Ho-Lee's binomial interest rate model I: from one- to multi-factor (with H. Aoki, and Y. Nagata) totally revised June 2006 arXiv math.PR/0606183 abstract: In this paper a multi-factor generalization of Ho-Lee model is proposed. In sharp contrast to the classical Ho-Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is stationary to be compatible with principal component analysis. Based on the model, generalizations of duration-based hedging are proposed. A continuous-time limit of the model is also discussed..

A discrete Ito calculus approach to He's framework for multi-factor discrete market.September, 2003. revised June 2006 arXiv math.PR/0606292 abstract: In the present paper, a discrete version of It\^o's formula for a class of multi-dimensional random walk is introduced and applied to the study of a discrete-time complete market model which we call He's framework. The formula unifies continuous-time and discrete-time settings and by regarding the latter as the finite difference scheme of the former, the order of convergence is obtained. The result shows that He's framework cannot be of order 1 scheme except for the one dimensional case.

Local time in Parisian walkways April, 2003, revised April 2006 arXiv math.PR/0604395 abstract:In the present paper, Ito formula and Tanaka formula for a special kind of symmetric random walk in the complex plain are studied. The random walk is called Parisian walk, and its local time is defined to be the number of exit from some regions.

Asymptotics of hedging errors in a slightly incomplete discrete market: a noise-sensitive example. April 2002 abstract: A slightly incomplete market where full information is not available is considered. In this market, targets are hedged by a very closely correlated security. Asymptotic behaviors of hedging errors as correlation tends to $ 1 $ are studied in connection with the theory of noise stability and sensitivity, and a noise-sensitive example that is orthogonal in the limit and hence cannot be hedged in any way is shown.

Quasi pricing of caps/floors and swaptions by quasi-Gaussian model. December 2000 (under revision)