Local Risk-Minimization for Defaultable Claims with Recovery Process

Abstract

We study the local risk-minimization approach for defaultable claims with random recovery at default time, seen as payment streams on the random interval t0, τ ∧ T u, where T denotes the fixed time-horizon. We find the pseudo-locally riskminimizing strategy in the case when the agent information takes into account the possibility of a default event (local risk-minimization with G-strategies) and we provide an application in the case of a corporate bond. We also discuss the problem of finding a pseudo-locally risk-minimizing strategy if we suppose the agent obtains her information only by observing the non-defaultable assets.

Local Risk Minimization for Defaultable Markets

“…The main contribution of this thesis is to collect and discuss extensively our results (see [1], [2], [3]), where, to the best of our knowledge, we have applied for the rst time in literature the local risk-minimization method to the pricing and hedging of defaultable claims.…”

“…a random recovery payment is received by the owner of the contract in case of default at time of 9 default. Here according to [3], we provide the pseudo-locally risk-minimizing strategy in the case when the agent information takes into account the possibility of a default event. We conclude by discussing the problem of nding a pseudo-locally risk-minimizing strategy in the case when the agent obtains her information only by observing the asset prices on the non-defaultable market before the default happens.…”

“…Here according to [3], we consider a general defaultable claim with random recovery at default time, represented by a predictable stochastic process. Our goal is to provide the pseudo-locally risk-minimizing strategy in the case when Moreover in Section 5.2.2 we discuss the problem of nding a pseudo-locally risk-minimizing strategy if we suppose the agent obtains her information only by observing the non-defaultable assets.…”

An optimal portfolio problem in a defaultable market

“…[1], [2], [3], [4], [14], [16], and [18]). Hou and Jin [16] studied an optimal investment problem with default risk under the conditional diversification assumption (which implies an asymptotic disappearance of the jump-risk premium), as in [15].…”

The Föllmer–Schweizer decomposition: Comparison and description

“…In fact, this technique has been used for hedging risks in different types of incomplete markets, such as the (life or non-life) insurance markets see for example [25,33] and the references therein, and defaultable markets see for example [5][6][7] and the reference therein. In most of these works, the authors formulate their local risk-minimization results based on the key fact that the FS-decomposition and the GKW-decomposition under the minimal martingale measure coincide.…”