Methods of Mathematical Finance-Springer (2001)

• Authors: Ioannis Karatzas, Steven E. Shreve
• Publisher: Springer New York
• Year of Publication: 2001
• Format: PDF
• Difficulty: ⭐⭐⭐⭐
• Recommendation Index: ⭐⭐⭐⭐⭐
• Download: [Click to download](https://asset.quant-wiki.com/pdf/Methods of Mathematical Finance-Springer (2001).pdf)

Introduction

This book is a sequel to "Brownian Motion and Stochastic Calculus" co-authored by Ioannis Karatzas and Steven E. Shreve. This book details contingent claim pricing and optimal consumption/investment strategies in complete and incomplete markets in the context of asset prices driven by Brownian motion. The book extends the theme of optimal consumption and investment to the study of complete market equilibrium, providing conditions for the existence and uniqueness of market prices that support transactions by heterogeneous agents.

This book covers core mathematical techniques and their applications in financial markets, including:

• Brownian motion model: Explores a market composed of N+1 financial assets, one of which is instantaneously risk-free (money market), and the remaining N are risky assets (stocks, commodities, or currencies).
• Valuation of Contingent Claims in Complete Markets: An introduction to methods for valuing derivative securities (contingent claims) whose value is derived from underlying securities such as stocks or bonds.
• Single agent consumption and investment: Solve the problem of how the agent consumes and invests under the initial endowment to maximize its expected consumption utility during the planning period or the wealth utility at the end of the period.
• Complete Market Equilibrium: A model is constructed in which security prices are determined by the law of supply and demand. Its basic elements are the endowment process and utility function of limited agents.
• Contingent Claims in Imperfect Markets: Discusses the arbitrage pricing and almost sure hedging of contingent claims when markets are incomplete due to portfolio constraints.

This book is intended to assist researchers who wish to apply advanced mathematics to the field of finance, with the material on optimal consumption and investment and market equilibrium geared toward the theoretical finance community, while the chapter on the valuation of contingent claims provides techniques of practical importance, particularly for the pricing of exotic options.

Main features

• Solid theoretical foundation
• Rich practical cases
• Clear operating instructions
• Suitable for practical applications

Suitable for the crowd

• Quantitative Analyst
• Algorithmic Trader
• Financial Engineer
• Data Scientist