We aim to obtain explicit representations of locally risk-minimizing of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein-Uhlenbeck type stochastic volatility models. Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets...

We focus on properties of the variance-optimal martingale measure for discontinuous semimartingales. In particular, we give sufficient conditions for the variance-optimal martingale measure to be a probability measure, and for the density process of the variance-optimal martingale measure to...

The aim of this paper is to give an extension of the mean-variance hedging problem to the $\mathcal{L}^p$-setting, where 1 p ∞. 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...

Mean-variance hedging for the discontinuous semimartingale case is obtained under some assumptions related to the variance-optimal martingale measure. In the present paper, two remarks on it are discussed. One is an extension of Hou–Karatzas' duality approach from the continuous case to...

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...

We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and lower bounds of good deal pricing bounds are expressed by...

We discuss the p-optimal martingale measure for p[set membership, variant](1,[infinity]) in continuous incomplete markets whose stock price is fluctuated by a d-dimensional continuous semimartingale. In this paper, we treat two simple models. One is a model where the mean-variance trade-off...