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THE GENERAL STRUCTURE OF OPTIMAL INVESTMENT AND CONSUMPTION WITH SMALL TRANSACTION COSTS
Author(s) -
Kallsen Jan,
MuhleKarbe Johannes
Publication year - 2017
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12106
Subject(s) - transaction cost , economics , consumption (sociology) , asset (computer security) , investment (military) , microeconomics , order (exchange) , database transaction , econometrics , computer science , finance , social science , programming language , computer security , sociology , politics , political science , law
We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time‐varying but small transaction costs, we derive simple formal asymptotics for the optimal policy and welfare. These reveal the roles of the investors' preferences as well as the market and cost dynamics, and also lead to a fully dynamic model for the implied trading volume. In frictionless models that can be solved in closed form, explicit formulas for the leading‐order corrections due to small transaction costs are obtained.