Precautionary Measures for Credit Risk Management in Jump Models

Abstract

Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely monitor its net worth as well as market conditions, and one of its important concerns is when to raise more capital so as not to violate capital adequacy requirements. In this paper, we model the tradeoff between avoiding costs of delay and premature capital raising, and solve the corresponding optimal stopping problem. In order to model defaults in a bank's loan/credit business portfolios, we represent its net worth by Levy processes, and solve explicitly for the double exponential jump diffusion process and for a general spectrally negative Levy process.

31 pages, 4 figures

References in corpus (3)

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• On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes
• Phase-type fitting of scale functions for spectrally negative Levy processes

Cited by in corpus (16)

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• Optimal Capital Structure with Scale Effects under Spectrally Negative Levy Models
• Inventory Control for Spectrally Positive Levy Demand Processes
• Contraction options and optimal multiple-stopping in spectrally negative Levy models
• Non-zero-sum optimal stopping game with continuous versus periodic exercise opportunities
• On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models
• Games of singular control and stopping driven by spectrally one-sided Levy processes
• An Excursion-Theoretic Approach to Regulator's Bank Reorganization Problem
• On the Bail-Out Optimal Dividend Problem
• Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities
• Refraction-reflection strategies in the dual model
• Optimality of doubly reflected Levy processes in singular control
• Optimality of multi-refraction dividend strategies in the dual model