On optimal approximation

1976 ◽  
pp. 220-225
Author(s):  
Arthur Sard
Keyword(s):  
Optimal Approximation

scholarly journals Optimal Approximation of Skorohod Integrals

2016 ◽  
Vol 31 (1) ◽  
pp. 206-231
Author(s):  
Andreas Neuenkirch ◽  
Peter Parczewski
Keyword(s):  
Optimal Approximation

Optimal approximation algorithm of feature coefficients and identification of target

1994 ◽  
Vol 11 (1) ◽  
pp. 57-63
Author(s):  
Liao Supeng ◽  
Li Xingguo ◽  
Fang Dagang
Keyword(s):  
Approximation Algorithm ◽  
Optimal Approximation

scholarly journals Distributional Replication

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1063
Author(s):  
Brendan K. Beare
Keyword(s):  
Hedge Fund ◽  
Minimum Cost ◽  
Random Variable ◽  
Optimal Approximation ◽  
Regularity Conditions ◽  
Return Distribution ◽  
Continuous Random Variable ◽  
Hedge Fund Replication ◽  
Market Index ◽  
Fund Return

A function which transforms a continuous random variable such that it has a specified distribution is called a replicating function. We suppose that functions may be assigned a price, and study an optimization problem in which the cheapest approximation to a replicating function is sought. Under suitable regularity conditions, including a bound on the entropy of the set of candidate approximations, we show that the optimal approximation comes close to achieving distributional replication, and close to achieving the minimum cost among replicating functions. We discuss the relevance of our results to the financial literature on hedge fund replication; in this case, the optimal approximation corresponds to the cheapest portfolio of market index options which delivers the hedge fund return distribution.

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