Related papers: Local risk-minimization for exponential additive p…
We illustrate how to compute local risk minimization (LRM) of call options for exponential L\'evy models. We have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast…
We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show…
We discuss the difference between locally risk-minimizing and delta hedging strategies for exponential L\'evy models, where delta hedging strategies in this paper are defined under the minimal martingale measure. We give firstly…
In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation…
We obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for…
Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model…
We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a…
In this paper we investigate the local risk-minimization approach for a semimartingale financial market where there are restrictions on the available information to agents who can observe at least the asset prices. We characterize the…
We provide a new algorithm for solving Risk Sensitive Partially Observable Markov Decisions Processes, when the risk is modeled by a utility function, and both the state space and the space of observations is finite. This algorithm is based…
We develop a numerical method for locally risk-minimizing (LRM) strategies for Barndorff-Nielsen and Shephard (BNS) models. Arai et al. (2017) derived a mathematical expression for LRM strategies in BNS models using Malliavin calculus for…
The purpose of this article is to introduce a new L\'evy process, termed Variance Gamma++ process, to model the dynamic of assets in illiquid markets. Such a process has the mathematical tractability of the Variance Gamma process and is…
The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least squares problems. In this work we study how a class of possible adaptations of this procedure can be used to solve maximum likelihood…
In this paper, we are concerned with centered Markov Additive Processes $\{(X_t,Y_t)\}_{t\in\T}$ where the driving Markov process $\{X_t\}_{t\in\T}$ has a finite state space. Under suitable conditions, we provide a local limit theorem for…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
The paper offers a unified approach to the study of three locally adaptive estimation methods in the context of univariate time series from both theoretical and empirical points of view. A general procedure for the computation of critical…
We apply a quadratic hedging scheme developed by Foellmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the…
This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by It\^o-L\'evy processes, but it also contains some new results on the underlying stochastic maximum…
The stochastic approximation EM algorithm (SAEM) is described for the estimation of item and person parameters given test data coded as dichotomous or ordinal variables. The method hinges upon the eigenanalysis of missing variables sampled…
This article deals with adaptive nonparametric estimation for L\'evy processes observed at low frequency. For general linear functionals of the L\'evy measure, we construct kernel estimators, provide upper risk bounds and derive rates of…
We investigate two hedging problems in exponential L\'evy models. First, we provide an explicit representation for the F\"ollmer--Schweizer decomposition of European type options under mild conditions, which implies a closed-form expression…