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Equal Risk Pricing Under Convex Trading Constraints
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Book Synopsis Equal Risk Pricing Under Convex Trading Constraints by : Ivan Guo
Download or read book Equal Risk Pricing Under Convex Trading Constraints written by Ivan Guo and published by . This book was released on 2015 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an incomplete market model where convex trading constraints are imposed upon the underlying assets, it is no longer possible to obtain unique arbitrage-free prices for derivatives using standard replication arguments. Most existing derivative pricing approaches involve the selection of a suitable martingale measure or the optimisation of utility functions as well as risk measures from the perspective of a single trader.We propose a new and effective derivative pricing method, referred to as the equal risk pricing approach, for markets with convex trading constraints. The approach analyses the risk exposure of both the buyer and seller of the derivative, and seeks an equal risk price which evenly distributes the expected loss for both parties under optimal hedging. The existence and uniqueness of the equal risk price are established for both European and American options. Furthermore, if the trading constraints are removed, the equal risk price agrees with the standard arbitrage-free price.Finally, the equal risk pricing approach is applied to a constrained Black-Scholes market model where short-selling is banned. In particular, simple pricing formulas are derived for European calls, European puts and American puts.
Book Synopsis Convex Measures of Risk and Trading Constraints by : Hans Föllmer
Download or read book Convex Measures of Risk and Trading Constraints written by Hans Föllmer and published by . This book was released on 2001 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hedging Derivatives by : Thorsten Rheinlander
Download or read book Hedging Derivatives written by Thorsten Rheinlander and published by World Scientific. This book was released on 2011 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Valuation and hedging of financial derivatives are intrinsically linked concepts. Choosing appropriate hedging techniques depends on both the type of derivative and assumptions placed on the underlying stochastic process. This volume provides a systematic treatment of hedging in incomplete markets. Mean-variance hedging under the risk-neutral measure is applied in the framework of exponential L(r)vy processes and for derivatives written on defaultable assets. It is discussed how to complete markets based upon stochastic volatility models via trading in both stocks and vanilla options. Exponential utility indifference pricing is explored via a duality with entropy minimization. Backward stochastic differential equations offer an alternative approach and are moreover applied to study markets with trading constraints including basis risk. A range of optimal martingale measures are discussed including the entropy, Esscher and minimal martingale measures. Quasi-symmetry properties of stochastic processes are deployed in the semi-static hedging of barrier options. This book is directed towards both graduate students and researchers in mathematical finance, and will also provide an orientation to applied mathematicians, financial economists and practitioners wishing to explore recent progress in this field."
Book Synopsis Hedging and Pricing with L2 Convex Risk Measures in Incomplete Markets by : Antoine Toussaint
Download or read book Hedging and Pricing with L2 Convex Risk Measures in Incomplete Markets written by Antoine Toussaint and published by . This book was released on 2007 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This framework is more suitable for optimal hedging with L 2 valued financial markets. A dual representation is given for this minimum risk when the risk measure is real-valued and we give an example of computation in a stochastic volatility model with the shortfall risk. In the general case when the risk may become infinite, we introduce constrained hedging and prove that the minimum risk is still an L2 convex risk measure and the existence of an optimal hedge.
Book Synopsis Multi-Period Trading Via Convex Optimization by : Stephen Boyd
Download or read book Multi-Period Trading Via Convex Optimization written by Stephen Boyd and published by . This book was released on 2017-07-28 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph collects in one place the basic definitions, a careful description of the model, and discussion of how convex optimization can be used in multi-period trading, all in a common notation and framework.
Book Synopsis Stochastic Finance by : Hans Föllmer
Download or read book Stochastic Finance written by Hans Föllmer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-25 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures
Book Synopsis Option Pricing, Interest Rates and Risk Management by : Elyès Jouini
Download or read book Option Pricing, Interest Rates and Risk Management written by Elyès Jouini and published by Cambridge University Press. This book was released on 2001 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 handbook surveys the state of practice, method and understanding in the field of mathematical finance. Every chapter has been written by leading researchers and each starts by briefly surveying the existing results for a given topic, then discusses more recent results and, finally, points out open problems with an indication of what needs to be done in order to solve them. The primary audiences for the book are doctoral students, researchers and practitioners who already have some basic knowledge of mathematical finance. In sum, this is a comprehensive reference work for mathematical finance and will be indispensable to readers who need to find a quick introduction or reference to a specific topic, leading all the way to cutting edge material.
Book Synopsis Convex Duality and Financial Mathematics by : Peter Carr
Download or read book Convex Duality and Financial Mathematics written by Peter Carr and published by Springer. This book was released on 2018-07-18 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization. Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims
Book Synopsis Essays on Portfolio Optimization and ESG Ratings under Risk Constraints and Incomplete Information by : Janke, Oliver
Download or read book Essays on Portfolio Optimization and ESG Ratings under Risk Constraints and Incomplete Information written by Janke, Oliver and published by Lehmanns Media. This book was released on with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we analyze various problems of dynamic portfolio optimization as well as green capital requirements under risk constraints and incomplete information. First, we examine the problem of optimal expected utility under the constraint of a utility-based shortfall risk measure in an incomplete market. The existence and uniqueness of an optimal solution to the problem are shown using a Lagrange multiplier and duality methods. Second, we consider the optimization problem under various levels of the investor’s information. By using martingale representation theorems, we demonstrate the existence and uniqueness of optimal solutions, which differ in their market dynamics. Third, we analyze the effects of green- and brownwashing on banks’ lending to firms, on the regulator’s deposit insurance subsidy, and on carbon emissions under different green capital requirement functions. Furthermore, we show that green capital requirements may compromise financial stability.
Book Synopsis Handbooks in Operations Research and Management Science: Financial Engineering by : John R. Birge
Download or read book Handbooks in Operations Research and Management Science: Financial Engineering written by John R. Birge and published by Elsevier. This book was released on 2007-11-16 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.
Book Synopsis The Market Price of Risk and Macro-Financial Dynamics by : Mr. Tobias Adrian
Download or read book The Market Price of Risk and Macro-Financial Dynamics written by Mr. Tobias Adrian and published by International Monetary Fund. This book was released on 2023-09-22 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose the conditional volatility of GDP spanned by financial factors as a “Volatility Financial Conditions Index” (VFCI) and show it is closely tied to the market price of risk. The VFCI exhibits superior explanatory power for stock and bond risk premia compared to other FCIs. We use a variety of identification strategies and instruments to demonstrate robust causal relationships between the VFCI and macroeconomic aggregates: a tightening of financial conditions as measured by the VFCI leads to a persistent contraction of output and triggers an immediate easing of monetary policy. Conversely, contractionary monetary policy shocks cause tighter financial conditions.
Book Synopsis Modeling and Simulation in Engineering, Economics, and Management by : María Ángeles Fernández-Izquierdo
Download or read book Modeling and Simulation in Engineering, Economics, and Management written by María Ángeles Fernández-Izquierdo and published by Springer. This book was released on 2013-06-01 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the refereed proceedings of the International Conference on Modeling and Simulation in Engineering, Economics, and Management, MS 2013, held in Castellón de la Plana, Spain, in June 2013. The event was co-organized by the AMSE Association and the SoGReS Research Group of the Jaume I University. This edition of the conference paid special attention to modeling and simulation in diverse fields of business management. The 28 full papers in this book were carefully reviewed and selected from 65 submissions. They are organized in topical sections on: modeling and simulation in CSR and sustainable development; modeling and simulation in finance and accounting; modeling and simulation in management and marketing; modeling and simulation in economics and politics; knowledge-based expert and decision support systems; and modeling and simulation in engineering.
Book Synopsis General Quadratic Risk Minimization by : Dian Zhu
Download or read book General Quadratic Risk Minimization written by Dian Zhu and published by . This book was released on 2016 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mean-variance portfolio selection and mean-variance hedging are mainstream research topics in mathematical nance, which can be subsumed within the framework of a general problem of quadratic risk minimization. We study this quadratic risk minimization problem in the setting of an It^o process market model with random market parameters. Our particular contribution is to introduce a combination of constraints on both the trading strategy (i.e. portfolio) and the wealth process, which includes in particular portfolio insurance in the form of a stipulated lower-bound on the wealth process over the entire trading interval (this is also called an American wealth constraint). The result is a stochastic control problem which includes the combination of a portfolio constraint (i.e. a \control constraint") and a wealth constraint over the trading interval (i.e. a \state constraint"). The goal of the present thesis is to address this stochastic control problem. Even in the setting of deterministic (or non-random) optimal control it is well known that a combination of control constraints and state constraints over the control interval presents some particular challenges, and of course these challenges increase considerably for stochastic control problems with the same combination of constraints. In this thesis we shall take advantage of the convexity of the problem and apply a powerful variational method of Rockafellar which has proved to be very e ective in the deterministic optimal control of partial di erential equations, convex optimization in continuum mechanics, and stochastic convex programming over nite dimensional spaces. The variational approach of Rockafellar enables one to systematically construct an appropriate vector space of dual variables, together with a dual problem on this space of dual variables, and gives conditions which ensure that there is zero duality gap (i.e. the values of the primal and dual problems are equal) as well as existence of a solution of the dual problem (i.e. existence of Lagrange multipliers for the constraints in the problem). The key to applying the Rockafellar variational approach to the stochastic control problem outlined above turns out to be a mild feasibility condition on the wealth process which is very reminiscent of \Slater-type" conditions familiar from convex optimization. With this condition in place we are able to construct an associated dual problem, and establish existence of a solution of the dual problem, together with Kuhn-Tucker optimality conditions which relate putative solutions of the primal and dual problems. We then use these optimality conditions to construct an optimal portfolio in terms of the solution of the dual problem.
Book Synopsis Stochastic Programming by : Horand Gassmann
Download or read book Stochastic Programming written by Horand Gassmann and published by World Scientific. This book was released on 2013 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.
Book Synopsis The Interval Market Model in Mathematical Finance by : Pierre Bernhard
Download or read book The Interval Market Model in Mathematical Finance written by Pierre Bernhard and published by Springer Science & Business Media. This book was released on 2012-12-14 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods. A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methods assembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics. The book is divided into five parts, which successively address topics including: · probability-free Black-Scholes theory; · fair-price interval of an option; · representation formulas and fast algorithms for option pricing; · rainbow options; · tychastic approach of mathematical finance based upon viability theory. This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.
Book Synopsis Mathematics of Derivative Securities by : Michael A. H. Dempster
Download or read book Mathematics of Derivative Securities written by Michael A. H. Dempster and published by Cambridge University Press. This book was released on 1997-10-13 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: During 1995 the Isaac Newton Institute for the Mathematical Sciences at Cambridge University hosted a six month research program on financial mathematics. During this period more than 300 scholars and financial practitioners attended to conduct research and to attend more than 150 research seminars. Many of the presented papers were on the subject of financial derivatives. The very best were selected to appear in this volume. They range from abstract financial theory to practical issues pertaining to the pricing and hedging of interest rate derivatives and exotic options in the market place. Hence this book will be of interest to both academic scholars and financial engineers.
Book Synopsis Multi-period Trading Via Convex Optimization by : Stephen P. Boyd
Download or read book Multi-period Trading Via Convex Optimization written by Stephen P. Boyd and published by . This book was released on 2017 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The single period method traces back to Markowitz; the multi-period methods trace back to model predictive control. Our contribution is to describe the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. In this paper, we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper.
