Actuarial and financial risk management in networks

Abstract

Interconnectedness constitutes a key characteristic of actuarial and financial systems. In regular times, it facilitates the provision of the systems’ important services to society. In times of crisis, however, it enables the spread of contagious distress that may adversely affect the overall economy and amplify crisis situations. In this thesis, we introduce and analyze two financial and one actuarial network model representing three particular risk management problems that arise from different forms of interconnectedness. First, we consider the spread of financial losses and defaults in a comprehensive model of a banking network. Distress therein may propagate through various forms of connections such as direct financial obligations, bankruptcy costs, fire sales, and cross-holdings. For the integrated financial market, we prove the existence of a price-payment equilibrium and design an algorithm for its computation. The corresponding number of defaults is analyzed in several comparative case studies. These illustrate the individual and joint impact of the considered interaction channels on systemic risk. Second, we study the problem of minimizing market inefficiencies, defined as deviations of realized asset prices from fundamental values, as a function of the network of banks’ overlapping asset portfolios. Prices are pressured from trading actions of the leverage targeting banks, which rebalance their portfolios in response to exogenous asset shocks. We prove the existence of a network of efficient asset holdings and characterize its properties and sensitivities. In particular, we find that the standard paradigm of asset portfolio diversification may cause tremendous market inefficiencies, especially during crisis situations. Third, we consider insurance against cyber epidemics. Infectious cyber threats, such as viruses and worms, diffuse within a network of possibly insured parties. Since the infection may affect many different agents at the same time, a provider of cyber insurance is exposed to significant accumulation risk. We build and analyze a stochastic model of losses generated by infectious cyber threats based on interacting particle systems and marked point processes. Together with a novel polynomial and mean-field approximation, our approach allows to explicitly compute prices for different forms of cyber insurance contracts. Numerical case studies demonstrate the impact of the network topology and indicate that higher order approximations are indispensable for the analysis of non-linear contracts.