We discuss the -Optimal Martingale Measure for ∈ (1, ∞) in continuous incomplete markets whose stock price is fluctuated by a -dimensional continuous semimartingale. In this paper, we treat two simple models. One is a model where the mean-variance trade-off process is deterministic. Another...

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...

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...

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...