Duality and equilibrium prices in economics of uncertainty

Adi Ben-Israel () and Aharon Ben-Tal ()

Mathematical Methods of Operations Research, 1997, vol. 46, issue 1, 85 pages

Abstract: A random variable (RV) X is given aminimum selling price $$S_U \left( X \right):=\mathop {\sup }\limits_x \left\{ {x + EU\left( {X - x} \right)} \right\}$$ and amaximum buying price $$B_p \left( X \right):=\mathop {\inf }\limits_x \left\{ {x + EP\left( {X - x} \right)} \right\}$$ whereU(·) andP(·) are appropriate functions. These prices are derived from considerations ofstochastic optimization with recourse, and are calledrecourse certainty equivalents (RCE's) of X. Both RCE's compute the “value” of a RV as an optimization problem, and both problems (S) and (B) have meaningful dual problems, stated in terms of theCsiszár φ-divergence $$I_\phi \left( {p,q} \right):=\sum\limits_{i=1}^n {q_i \phi \left( {\frac{{p_i }}{{q_i }}} \right)} $$ a generalized entropy function, measuring the distance between RV's with probability vectors p and q. The RCES U was studied elsewhere, and applied to production, investment and insurance problems. Here we study the RCEB P , and apply it to problems ofinventory control (where the attitude towards risk determines the stock levels and order sizes) andoptimal insurance coverage, a problem stated as a game between the insurance company (setting the premiums) and the buyer of insurance, maximizing the RCE of his coverage. Copyright Physica-Verlag 1997

Keywords: Stochastic Optimization with Recourse; Decision-making under Uncertainty; Certainty Equivalents; Risk Aversion; Inventory Control; Insurance (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/BF01199463 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:46:y:1997:i:1:p:51-85

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/BF01199463

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().