Asymptotic Analysis for Optimal Investment and Consumption with Transaction Costs with Two Futures Contracts
Author: Maxim Bichuch
Publisher:
Published: 2010
Total Pages: 0
ISBN-13:
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Author: Maxim Bichuch
Publisher:
Published: 2010
Total Pages: 0
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DOWNLOAD EBOOKAuthor: Fred Espen Benth
Publisher: Springer
Published: 2013-07-11
Total Pages: 326
ISBN-13: 3319004131
DOWNLOAD EBOOKThe current volume presents four chapters touching on some of the most important and modern areas of research in Mathematical Finance: asset price bubbles (by Philip Protter); energy markets (by Fred Espen Benth); investment under transaction costs (by Paolo Guasoni and Johannes Muhle-Karbe); and numerical methods for solving stochastic equations (by Dan Crisan, K. Manolarakis and C. Nee).The Paris-Princeton Lecture Notes on Mathematical Finance, of which this is the fifth volume, publish cutting-edge research in self-contained, expository articles from renowned specialists. The aim is to produce a series of articles that can serve as an introductory reference source for research in the field.
Author: Maxim Bichuch
Publisher:
Published: 2014
Total Pages: 58
ISBN-13:
DOWNLOAD EBOOKAn agent invests in two types of futures contracts, whose prices are possibly correlated arithmetic Brownian motions, and invests in a money market account with a constant interest rate. The agent pays a transaction cost for trading in futures proportional to the size of the trade. She also receives utility from consumption. The agent maximizes expected infinite-horizon discounted utility from consumption. We determine the first two terms in the asymptotic expansion of the value function in the transaction cost parameter around the known value function for the case of zero transaction cost. The method of solution when the futures are uncorrelated follows a method used previously to obtain the analogous result for one risky asset. However, when the futures are correlated, a new methodology must be developed. It is suspected in this case that the value function is not twice continuously differentiable, and this prevents application of the former methodology.
Author: Jin Hyuk Choi
Publisher:
Published: 2012
Total Pages: 186
ISBN-13:
DOWNLOAD EBOOKWe revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellman equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. By analyzing the properties of the free boundary problem, we provide an explicit characterization of model parameters for which the value function is finite. Furthermore, we prove that the value function, as well as the slopes of the lines demarcating the no-trading region, can be expanded as a series of integer powers of [lambda superscript 1/3]. The coefficients of arbitrary order in this expansion can be computed.
Author: Thaleia Zariphopoulou
Publisher:
Published: 1989
Total Pages: 136
ISBN-13:
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Published: 2005
Total Pages: 796
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ISBN-13: 9783037191736
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Published: 2015
Total Pages: 109
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Published: 1996
Total Pages: 508
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DOWNLOAD EBOOKAuthor: Jean Louis Heck
Publisher:
Published: 1996
Total Pages: 498
ISBN-13: 9780070277908
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