Takuji Arai

Lectures

I have charge of the following lectures:

Title	Semester	Language	Materials
Mathematical Analysis 2a	Spring	Japanese	Lecture Note (in Japanese) Exercise (in Japanese) Solutions for Exercise (in Japanese) Assignment (in Japanese) Solutions for assignment and exam (in Japanese)
Introduction to Finance (PCP)	Fall	English	Lecture note

Grants

My research is supported by Scientific Research (C) No.18K03422.

Ongoing Research Projects

Quadratic hedging for Levy markets and jump-type stochastic volatility models via Malliavin calculus and their numerical analysis
Convex risk measures related to certainty equivalence

Preprints

A Clark-Ocone type formula via Ito calculus and its application to finance (with R. Suzuki). arXiv
Pricing and hedging of VIX options for Barndorff-Nielsen and Shephard models. arXiv

Publications

Optimal initial capital induced by the optimized certainty equivalent, Insurance: Mathematics and Economics vol.85, pp.115-125, 2019 (with T. Asano and K. Nishide). discussion paper
A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus, Applied Mathematical Finance vol.25, pp.247-267, 2018 (with Y. Imai). arXiv
Numerical analysis on quadratic hedging strategies for normal inverse Gaussian models, Advances in Mathematical Economics vol.22, pp.1-24, 2018 (with Y. Imai and R. Nakashima). arXiv
On the difference between locally risk-minimizing and delta hedging strategies for exponential Levy models, Japan Journal of Industrial and Applied Mathematics vol.34, pp.845-858, 2017 (with Y. Imai). arXiv
Good deal bounds with convex constraints, International Journal of Theoretical and Applied Finance, vol.20, 1750011, 2017. previous version(arXiv) extended version
Local risk-minimization for Barndorff-Nielsen and Shephard models, Finance & Stochastics, vol.21, pp.551-592, 2017 (with Y. Imai and R. Suzuki). arXiv
Local risk-minimization for Barndorff-Nielsen and Shephard models with volatility risk premium, Advances in Mathematical Economics, vol.20, pp.3-22, 2016. arXiv
Numerical analysis on local risk-minimization for exponential Levy models, International Journal of Theoretical and Applied Finance vol.19, 1650008, 2016 (with Y. Imai and R. Suzuki). arXiv
Comparison of local risk minimization and delta hedging strategy for exponential Levy models, JSIAM Letters, vol.7, pp.77-80, 2015 (with Y. Imai).
Local risk-minimization for Levy markets, International Journal of Financial Engineering, vol.2, 1550015, 2015 (with R. Suzuki).
Convex risk measures for cadlag processes on Orlicz spaces, SIAM Journal on Financial Mathematics, vol.5, pp.609-625, 2014.
Minimization of hedging error on Orlicz space, Proceedings of Actuarial and Financial Mathematics Conference, 2014, pp.3-14, 2014 (with T. Choulli).
Convex risk measures for good deal bounds, Mathematical Finance, vol.24, pp.464-484, 2014 (with M. Fukasawa).
Good deal bounds induced by shortfall risk, SIAM Journal on Financial Mathematics, vol.2, pp.1-21, 2011.
How much can investors discount?, Advances in Mathematical Economics, vol.14, pp.1-16, 2011 (with T. Suzuki).
Convex risk measures on Orlicz spaces: inf-convolution and shortfall, Mathematics and Financial Economics, vol.3, pp.73-88, 2010.
q-optimal martingale measures for discrete time models, Asia Pacific Financial Markets, vol.15, pp.155-173, 2008 (with M. Kawaguchi).
L^p-projections of random variables and its application to finance, International Journal of Theoretical and Applied Finance, vol.11, pp.869-888, 2008.
Optimal hedging strategies on asymmetric functions, Advances in Mathematical Economics, vol.11, pp.1-10, 2008.
An approximate approach to the exponential utility indifference valuation, International Journal of Theoretical and Applied Finance, vol.10, pp.475-503, 2007.
Some properties of the variance-optimal martingale measure for discontinuous semimartingales, Statistics & Probability Letters, vol.74, pp.163-170, 2005.
Some remarks on mean-variance hedging for discontinuous asset price processes, International Journal of Theoretical and Applied Finance, vol.8, pp.425-443, 2005.
An extension of mean-variance hedging to the discontinuous case, Finance & Stochastics, vol.9, pp.129-139, 2005.
Minimal martingale measures for jump diffusion processes, Journal of Applied Probability, vol.41, pp.263-270, 2004.
Mean-variance hedging for discontinuous semimartingales, Tokyo Journal of Mathematics, vol.25, pp.435-452, 2002.
The p-optimal martingale measure in continuous trading models, Statistics & Probability Letters, vol.54, pp.93-99, 2001.
The relations between minimal martingale measure and minimal entropy martingale measure, Asia Pacific Financial Markets, vol.8, pp.167-177, 2001.
A class of semi-selfsimilar processes related to random walks in random scenery, Tokyo Journal of Mathematics, vol.24, pp.69-85, 2001.