Mathematical finance

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Inhaltsverzeichnis (Note: co-authored paper titles feature the lecturer’s name in bold). Preface. Participants. The text explores various financial concepts, including an online portfolio strategy with predictive elements and the dynamics of continuous-time financial markets, focusing on transaction costs and intensity. It examines demand heterogeneity and its impact on price volatility, alongside optimal default boundaries in discrete time settings. The work presents an infinite factor model for interest rate derivatives and discusses arbitrage and pricing with collateral. It delves into optimal controls for singular stochastic control problems and quadratic approaches to interest rate models in incomplete markets. Empirical examples of risk-sensitive asset management are provided. The text also covers bounded variation singular stochastic control, option pricing under Lévy processes, and static hedging strategies. Further topics include fractional Brownian motion in financial modeling, stochastic volatility, and mutual debts compensation through graph theory. The work introduces concepts in stochastic finance, fractional calculus, and new developments in backward stochastic Riccati equations. It discusses quantile hedging in jump-diffusion markets, optimal consumption with partial observation, and liquidity risk in energy markets. Additionally, it addresses mean-variance portfolio selections, transaction processes among trad