Titlebook: Mathematical Finance; Ernst Eberlein,Jan Kallsen Book 2019 Springer Nature Switzerland AG 2019 91G20, 91G80, 60G51, 60G44.60H05, 60J75, 60

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Optimal ControlDynamic stochastic optimisation problems play an important role in Mathematical Finance and other applications. In this chapter we provide basic tools for their mathematical treatment in continuous time.

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Equity ModelsThe theory of Mathematical Finance in the following chapters rests on price processes of assets such as stocks, currencies, bonds, and commodities. They are often assumed to be given exogenously. Therefore we start by discussing what kinds of processes are suggested by statistical properties of real data.

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Markets, Strategies, ArbitrageWe study several problems of Mathematical Finance in a common framework, which is laid down in this chapter. We start by introducing notions such as price processes, trading strategies, discounting, and dividends.

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Optimal InvestmentAs an investor in a securities market you have to decide how to arrange your portfolio. In this chapter we consider the natural situation that you want to maximise your profits. It is not entirely obvious how to formalise this goal because the payoff of investments is typically random.

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Utility-Based Valuation and Hedging of DerivativesValuation based on quadratic hedging is easy to understand and mathematically tractable compared to other approaches. Its economic justification is less obvious.

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