{'fraction_non_alphanumeric': 0.015248551387618176, 'fraction_numerical': 0.002439768222018908, 'mean_word_length': 5.23574144486692, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Measures and models of financial risk

In this thesis, we study monetary measures and endogenous models of financial risk. The first part considers two aspects of the quantification of financial risk. We focus on the one hand on the calculation of risk measurements by Monte Carlo simulation. On the other hand, we investigate a particular class of dynamic risk measures. In the second part we analyze two models of financial risk in economies with interacting agents. First, we focus on credit contagion of firms which interact with each other in a network of business partners. Second, we investigate the market interaction of investors with bounded rationality in an evolutionary selection market model. The simulation of distributions of the value of financial positions is an important issue for financial institutions. If risk measures are evaluated for a simulated distribution instead of the model-implied distribution, the probability of errors of risk measurements need to be analyzed. This topic is investigated in Chapter 1. For distribution-invariant risk measures which are continuous on compacts and for value at risk we derive large deviation bounds. If the approximate risk measurements are based on the empirical distribution of independent samples, the rate function equals the minimal relative entropy under a risk measure constraint. For average value at risk (AVaR) and shortfall risk we solve this minimization problem explicitly. Chapter 2 provides an axiomatic characterization of dynamic risk measures. We prove a representation theorem and investigate the connection to static risk measures. Two notions of dynamic consistency are proposed. A key insight is that dynamic consistency and the notion of measure convex sets of probability measures are intimately related. Measure convexity can be interpreted using the concept of compound lotteries. This leads to a characterization of a class of static risk measures closely connected to shortfall risk. Chapter 3 investigates credit contagion. Credit contagion refers to the propagation of economic distress from one firm to another. Using methods from the theory of interacting particle systems, we propose a model for these contagion phenomena, assuming they are due to the local interaction of firms in a business partner network. We study aggregate credit losses on large portfolios of financial positions contracted with firms subject to credit contagion. In particular, we provide an explicit Gaussian approximation of the distribution of portfolio losses. We find that contagion processes induce additional fluctuations of losses around their averages, whose size depends on the denseness of the business partner network. In Chapter 4 we derive a continuous time approximation of the evolutionary market selection model of Blume and Easley (1992). Conditions on the payoff structure of the assets are identified that guarantee convergence. We prove that the continuous time approximation equals the solution of an integral equation in a random environment. For constant asset returns, it reduces to an autonomous ordinary differential equation. We study its long-run behavior using techniques related to Lyapunov functions, and compare our results to the benchmark of profit-maximizing investors.