Capital Minimization as a Market Objective

28 January 2011
Dr Dilip Madan
The static two price economy of conic finance is first employed to define capital, profit, and subsequently return and leverage. Examples illustrate how profits are negative on claims taking exposure to loss and positive on claims taking gain exposure. It is argued that though markets do not have preferences or objectives of their own, competitive pressures lead markets to become capital minimizers or leverage maximizers. Yet within a static context one observes that hedging strategies must then depart from delta hedging and incorporate gamma adjustments. Finally these ideas are generalized to a dynamic context where for dynamic conic finance, the bid and ask price sequences are seen as nonlinear expectation operators associated with the solution of particular backward stochastic difference equations (BSDE) solved in discrete time at particular tenors leading to tenor specific or equivalently liquidity contingent pricing. The drivers of the associated BSDEs are exhibited in complete detail.