A discrete-time benchmark tracking problem in two markets subject to random environments

In this manuscript, we study a benchmark tracking problem when prices evolve through a Binomial model with a random environment. The agent invests a given fund’s capital into different assets in a predetermined market to replicate at each stage of time a financial index or benchmark. To measure the...

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Vydané v:OR Spectrum Ročník 46; číslo 4; s. 1265 - 1294
Hlavní autori: Jasso-Fuentes, Héctor, Salgado-Suárez, Gladys D.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2024
Springer Nature B.V
Predmet:
Bankruptcy
Benchmarks
Business and Management
Calculus of Variations and Optimal Control; Optimization
Derivatives
Deviation
Dynamic programming
Error analysis
Index funds
Investment strategy
Investments
Investors
Mathematics
Operations Research/Decision Theory
Original Article
Quadratic equations
Time measurement
Tracking problem
Valuation
Random environment
90C40
Random walks
91G15
82B41
Benchmark tracking problems
60K37
Decision processes
93C30
ISSN:0171-6468, 1436-6304
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Shrnutí:In this manuscript, we study a benchmark tracking problem when prices evolve through a Binomial model with a random environment. The agent invests a given fund’s capital into different assets in a predetermined market to replicate at each stage of time a financial index or benchmark. To measure the actual deviation between the agent’s wealth and the current benchmark, we apply a deviation error expressed as a total sum of quadratic functions. We also assume the agent is obligated to change her/his investment between two markets when it is mandatory. This obligation happens when the fund’s wealth falls down a predetermined bankruptcy barrier. The dynamic programming method is then used to get optimal investment strategies that minimize the deviation error as well as to characterize the minimum deviation. We also apply the so-called potential function to analyze the influence of the environment on the prices. Numerical simulations are provided to illustrate our results.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0171-6468
1436-6304
DOI:10.1007/s00291-024-00767-x