Local Risk-Minimization for Payment Processes: Application to Insurance Contracts with Surrender Option or to Default Sensitive Contingent Claims

2008 ◽  
Author(s):  
Jérôme Barbarin
Keyword(s):  
Contingent Claims ◽  
Risk Minimization ◽  
Insurance Contracts ◽  
Local Risk

Local risk minimization and numéraire

1999 ◽  
Vol 36 (04) ◽  
pp. 1126-1139 ◽  
Author(s):  
F. Biagini ◽  
M. Pratelli
Keyword(s):  
Stochastic Process ◽  
Stochastic Volatility ◽  
Contingent Claims ◽  
Continuous Case ◽  
Risk Minimization ◽  
Complete Markets ◽  
Local Risk ◽  
The Right

The ‘change of numéraire’ technique has been introduced by Geman, El Karoui and Rochet for pricing and hedging contingent claims in the case of complete markets. In this paper we study the ‘change of numéraire’ using the ‘locally risk-minimizing approach’, when the market is not complete. We prove that, if the stochastic process which represents the prices is continuous, the l.r.m. strategy is invariant by a change of numéraire (this result is false in the right-continuous case, as is shown by some counterexamples). We also give an extension of Merton's formula to the case of stochastic volatility.

NUMERICAL ANALYSIS ON LOCAL RISK-MINIMIZATION FOR EXPONENTIAL LÉVY MODELS

2016 ◽  
Vol 19 (02) ◽  
pp. 1650008 ◽  
Author(s):  
TAKUJI ARAI ◽  
YUTO IMAI ◽  
RYOICHI SUZUKI
Keyword(s):  
Incomplete Markets ◽  
Contingent Claims ◽  
Risk Minimization ◽  
Gamma Model ◽  
Variance Gamma ◽  
Call Options ◽  
Estimated Parameters ◽  
Exponential Lévy Models ◽  
Local Risk ◽  
Variance Gamma Model

We illustrate how to compute local risk minimization (LRM) of call options for exponential Lévy models. Here, LRM is a popular hedging method through a quadratic criterion for contingent claims in incomplete markets. Arai & Suzuki (2015) have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform (FFT) method suggested by by Carr & Madan (1999). Considering Merton jump-diffusion models and variance gamma models as typical examples of exponential Lévy models, we provide the forms for the FFT explicitly; and compute the values of LRM numerically for given parameter sets. Furthermore, we illustrate numerical results for a variance gamma model with estimated parameters from the Nikkei 225 index.

scholarly journals Locally Risk-minimizing Hedging of Insurance Payment Streams

2007 ◽  
Vol 37 (1) ◽  
pp. 67-91 ◽  
Author(s):  
Martin Riesner
Keyword(s):  
Financial Market ◽  
Life Insurance ◽  
Levy Process ◽  
Contingent Claim ◽  
Risk Minimization ◽  
Hedging Strategy ◽  
Insurance Contracts ◽  
Insurance Payment ◽  
Local Risk ◽  
Martingale Case

For the martingale case Föllmer and Sondermann (1986) introduced a unique admissible risk-minimizing hedging strategy for any square-integrable contingent claim H. Schweizer (1991) developed their theory further to the semimartingale case introducing the notion of local risk-minimization. Møller (2001) extended the theory of Föllmer and Sondermann (1986) to hedge general payment processes occurring mainly in insurance. We expand local risk-minimization to the theory of hedging general payment processes and derive such a hedging strategy for general unit-linked life insurance contracts in a general Lévy process financial market.

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