Titlebook: Methods of Mathematical Finance; Ioannis Karatzas,Steven E. Shreve Book 1998 Springer-Verlag New York 1998 Brownian motion.Stochastic calc

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https://doi.org/10.1007/978-1-4939-6845-9Brownian motion; Stochastic calculus; agents; equilibrium; finance; incomplete markets; mathematical finan

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A Brownian Model of Financial Markets,Throughout this monograph we deal with a financial market consisting of N + 1 financial assets. One of these assets is instantaneously risk-free, and will be called a money market. Assets 1 through N are risky, and will be called stocks (although in applications of this model they are often commodities or currencies, rather than common stocks).

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Equilibrium in a Complete Market,In the context of continuous-time financial markets, the equilibrium problem is to build a model in which security prices are determined by the law of supply and demand. The primitives in this model are the endowment processes and the utility functions of a finite number of agents.

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Contingent Claim Valuation in a Complete Market,om the value of another underlying, more basic, security, such as a stock or a bond. Common derivative securities are put options, call options, forward contracts, futures contracts, and swaps. These securities can be used for both speculation and hedging, but their creation and marketing are based much more on the latter use than the former.

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Single-Agent Consumption and Investment,et as set forth in Chapter 1. The objective of this agent is to maximize the expected utility of consumption over the planning horizon, or to maximize the expected utility of wealth at the end of the planning horizon, or to maximize some combination of these two quantities.

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