2. The potential decline of the portfolio value below some critical limit is an important issue in portfolio selection. synthetic option strategy is a strategy adopted by large institutional investors in which available resources are used to articially prrsluce the desired payoff structure. Let W" be the investor's initial wealth, T be the planning horizon. R be the riskless return for one period, Iii}- he the (random) return for asset i = 1, - - - , N at time i. Let 1: denote the value of the portfolio at the end of the planning horizon. and 3:} denote the amount of wealth allocated to asset i at time 1:. Assume that the transaction cost are ii for all assets at all time. To construct the desired synthetic option. 1: is split into a detenrrinistic component representing the riskless value of the portfolio Z and a surplus z E i] which is a random variable that depends on the scenarios (random events). Thus. given the investor's risk aversion parameter p. 2 1. the investor's synthetic option strategy solves the following problem: E Z, .'.t. = Z 'v' Q ragga} [z] + pr. s z\