Dynamic Programming Equations

2001 ◽  
pp. 53-66 ◽  
Author(s):  
Harold J. Kushner ◽  
Paul Dupuis
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Equations

Non-negative matrices, dynamic programming and a harvesting problem

1984 ◽  
Vol 21 (04) ◽  
pp. 685-694 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Dynamic Programming ◽  
Asymptotic Behaviour ◽  
Small Population ◽  
Asymptotic Behaviour Of Solutions ◽  
Survival Potential ◽  
Dynamic Programming Equations

Existing results on the asymptotic behaviour of solutions to two dynamic programming equations involving non-negative matrices are reviewed and strengthened in certain directions. The results are then applied to strategies for harvesting of a small population so as to optimise its survival potential in a limited environment.

scholarly journals ALGORITHMIC TRADING WITH LEARNING

2016 ◽  
Vol 19 (04) ◽  
pp. 1650028 ◽  
Author(s):  
ÁLVARO CARTEA ◽  
SEBASTIAN JAIMUNGAL ◽  
DAMIR KINZEBULATOV
Keyword(s):  
Adverse Effect ◽  
Dynamic Programming ◽  
Numerical Scheme ◽  
Algorithmic Trading ◽  
Limit Orders ◽  
Optimal Mix ◽  
Systems Of Pdes ◽  
Dynamic Programming Equations ◽  
Proof Of Convergence ◽  
Future Date

We propose a model where an algorithmic trader takes a view on the distribution of prices at a future date and then decides how to trade in the direction of their predictions using the optimal mix of market and limit orders. As time goes by, the trader learns from changes in prices and updates their predictions to tweak their strategy. Compared to a trader who cannot learn from market dynamics or from a view of the market, the algorithmic trader’s profits are higher and more certain. Even though the trader executes a strategy based on a directional view, the sources of profits are both from making the spread as well as capital appreciation of inventories. Higher volatility of prices considerably impairs the trader’s ability to learn from price innovations, but this adverse effect can be circumvented by learning from a collection of assets that comove. Finally, we provide a proof of convergence of the numerical scheme to the viscosity solution of the dynamic programming equations which uses new results for systems of PDEs.

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