The Economics of Continuous-Time Finance

The Economics of Continuous-Time Finance
Author: Bernard Dumas
Publisher: MIT Press
Total Pages: 641
Release: 2017-10-27
Genre: Business & Economics
ISBN: 0262036541

An introduction to economic applications of the theory of continuous-time finance that strikes a balance between mathematical rigor and economic interpretation of financial market regularities. This book introduces the economic applications of the theory of continuous-time finance, with the goal of enabling the construction of realistic models, particularly those involving incomplete markets. Indeed, most recent applications of continuous-time finance aim to capture the imperfections and dysfunctions of financial markets—characteristics that became especially apparent during the market turmoil that started in 2008. The book begins by using discrete time to illustrate the basic mechanisms and introduce such notions as completeness, redundant pricing, and no arbitrage. It develops the continuous-time analog of those mechanisms and introduces the powerful tools of stochastic calculus. Going beyond other textbooks, the book then focuses on the study of markets in which some form of incompleteness, volatility, heterogeneity, friction, or behavioral subtlety arises. After presenting solutions methods for control problems and related partial differential equations, the text examines portfolio optimization and equilibrium in incomplete markets, interest rate and fixed-income modeling, and stochastic volatility. Finally, it presents models where investors form different beliefs or suffer frictions, form habits, or have recursive utilities, studying the effects not only on optimal portfolio choices but also on equilibrium, or the price of primitive securities. The book strikes a balance between mathematical rigor and the need for economic interpretation of financial market regularities, although with an emphasis on the latter.

Optimal Portfolios

Optimal Portfolios
Author: Ralf Korn
Publisher: World Scientific
Total Pages: 352
Release: 1997
Genre: Business & Economics
ISBN: 9812385347

The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.

Controlled Markov Processes and Viscosity Solutions

Controlled Markov Processes and Viscosity Solutions
Author: Wendell H. Fleming
Publisher: Springer Science & Business Media
Total Pages: 436
Release: 2006-02-04
Genre: Mathematics
ISBN: 0387310711

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

Portfolio Selection in Continuous Time

Portfolio Selection in Continuous Time
Author: Constantin Alexandru Filitti
Publisher:
Total Pages: 134
Release: 2004
Genre: Portfolio-Management / Dynamische Optimierung / Betriebswirtschaftliche Investitionstheorie / Stochastischer Prozess
ISBN:

Portfolio Selection and Asset Pricing: Models of Financial Economics and Their Applications in Investing

Portfolio Selection and Asset Pricing: Models of Financial Economics and Their Applications in Investing
Author: Jamil Baz
Publisher: McGraw Hill Professional
Total Pages: 426
Release: 2022-09-06
Genre: Business & Economics
ISBN: 126427016X

This uniquely comprehensive guide provides expert insights into everything from financial mathematics to the practical realities of asset allocation and pricing Investors like you typically have a choice to make when seeking guidance for portfolio selection―either a book of practical, hands-on approaches to your craft or an academic tome of theories and mathematical formulas. From three top experts, Portfolio Selection and Asset Pricing strikes the right balance with an extensive discussion of mathematical foundations of portfolio choice and asset pricing models, and the practice of asset allocation. This thorough guide is conveniently organized into four sections: Mathematical Foundations―normed vector spaces, optimization in discrete and continuous time, utility theory, and uncertainty Portfolio Models―single-period and continuous-time portfolio choice, analogies, asset allocation for a sovereign as an example, and liability-driven allocation Asset Pricing―capital asset pricing models, factor models, option pricing, and expected returns Robust Asset Allocation―robust estimation of optimization inputs, such as the Black-Litterman Model and shrinkage, and robust optimizers Whether you are a sophisticated investor or advanced graduate student, this high-level title combines rigorous mathematical theory with an emphasis on practical implementation techniques.

A Perturbation Approach to Continuous-Time Portfolio Selection

A Perturbation Approach to Continuous-Time Portfolio Selection
Author: Dietmar Leisen
Publisher:
Total Pages: 38
Release: 2016
Genre:
ISBN:

This paper studies portfolio selection in continuous-time models with stochastic investment opportunities. We consider asset allocation problems where preferences are specified as power utility derived from terminal wealth as well as consumption-savings problems with recursive utility Epstein-Zin preferences. The paper approximates the associated dynamic programming problem by perturbing the coefficients of the stochastic dynamics. We represent the Hamilton-Jacobi-Bellman equation as a series of partial differential equations that can be solved iteratively in closed-form through computer algebra software, at any desired accuracy.

Continuous-time Stochastic Control and Optimization with Financial Applications

Continuous-time Stochastic Control and Optimization with Financial Applications
Author: Huyên Pham
Publisher: Springer Science & Business Media
Total Pages: 243
Release: 2009-05-28
Genre: Mathematics
ISBN: 3540895000

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Continuous-Time Asset Pricing Theory

Continuous-Time Asset Pricing Theory
Author: Robert A. Jarrow
Publisher: Springer Nature
Total Pages: 470
Release: 2021-07-30
Genre: Business & Economics
ISBN: 3030744108

Asset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features ​new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. Taking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book’s underlying theme of economic bubbles. Written by a leading expert in risk management, Continuous-Time Asset Pricing Theory is the first textbook on asset pricing theory with a martingale approach. Based on the author’s extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background.

Big Data Challenges of High-Dimensional Continuous-Time Mean-Variance Portfolio Selection and a Remedy

Big Data Challenges of High-Dimensional Continuous-Time Mean-Variance Portfolio Selection and a Remedy
Author: Mei Choi Chiu
Publisher:
Total Pages: 34
Release: 2017
Genre:
ISBN:

Investors interested in the global financial market have to analyze financial securities internationally. The optimal global investment decision involves processing a huge amount of data for a high-dimensional portfolio. This paper investigates the big data challenges of two mean-variance optimal portfolios: continuous-time precommitment and constant-rebalancing strategies. We show that both optimized portfolios implemented with the traditional sample estimates converge to the worst performing portfolio when the portfolio size becomes large. The crux of the problem is the estimation error accumulated from the huge dimension of stock data. We then propose a linear programming optimal (LPO) portfolio framework, which applies a constrained l1 minimization to the theoretical optimal control to mitigate the risk associated with the dimensionality issue. The resulting portfolio becomes a sparse portfolio that selects stocks with a data-driven procedure and hence offers a stable mean-variance portfolio in practice. When the number of observations becomes large, the LPO portfolio converges to the oracle optimal portfolio, which is free of estimation error, even though the number of stocks grows faster than the number of observations. Our numerical and empirical studies demonstrate the superiority of the proposed approach.

Strategic Asset Allocation

Strategic Asset Allocation
Author: John Y. Campbell
Publisher: OUP Oxford
Total Pages: 272
Release: 2002-01-03
Genre: Business & Economics
ISBN: 019160691X

Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.