Related papers: Hedging of defaultable claims in a structural mode…
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…
The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular,…
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time…
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
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…
We study the hedging and valuation of European and American claims on a non-traded asset $Y$, when a traded stock $S$ is available for hedging, with $S$ and $Y$ following correlated geometric Brownian motions. This is an incomplete market,…
We compare two models of corporate default by calculating the Jeffreys-Kullback-Leibler divergence between their predicted default probabilities when asset correlations are either high or low. Our main results show that the divergence…
In this paper we study the pricing and hedging of nonreplicable contingent claims, such as long-term insurance contracts like variable annuities. Our approach is based on the benchmark-neutral pricing framework of Platen (2024), which…
We propose a unified structural credit risk model incorporating both insolvency and illiquidity risks, in order to investigate how a firm's default probability depends on the liquidity risk associated with its financing structure. We assume…
Measuring the corporate default risk is broadly important in economics and finance. Quantitative methods have been developed to predictively assess future corporate default probabilities. However, as a more difficult yet crucial problem,…
In the present work we address the problem of evaluating the historical performance of a trading strategy or a certain portfolio of assets. Common indicators such as the Sharpe ratio and the risk adjusted return have significant drawbacks.…
In this article we consider the surplus process of an insurance company within the Cramer-Lundberg framework. We study the optimal reinsurance strategy and dividend distribution of an insurance company under proportional reinsurance, in…
This paper presents how to apply the stochastic collocation technique to assets that can not move below a boundary. It shows that the polynomial collocation towards a lognormal distribution does not work well. Then, the potentials issues of…
This paper studies the stochastic modeling of market drawdown events and the fair valuation of insurance contracts based on drawdowns. We model the asset drawdown process as the current relative distance from the historical maximum of the…
This paper studies a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. We propose a fixed point approach to analyze the mark-to-market contract value with…
We consider option hedging in a model where the underlying follows an exponential L\'evy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The…
In this paper we consider a multivariate risk model with common renewal process, while the logarithmic returns of the insurers investment portfolio, are described by a Levy process. In the two main results are established an asymptotic…
Models trained under assumptions in the complete market usually don't take effect in the incomplete market. This paper solves the hedging problem in incomplete market with three sources of incompleteness: risk factor, illiquidity, and…
Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber-Shiu functions) in a Cramer-Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modelled as…
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…