Patent ID: 8768810

Claim:
A method for dynamic asset allocation for optimization of a given portfolio of assets using a known initial wealth level as well as a given investor risk aversion with respect to wealth at the end of the investor's investment horizon, comprising the steps of: approximating the investor's risk aversion function with respect to wealth by computing absolute risk aversions α i by one or more computers, that represent a function of risk aversion versus wealth by determining coefficients of a piecewise exponential function with K pieces, where each piece represents a certain absolute risk aversion α i , where i=1, . . . , K, K<∞, for a preselected number of discrete absolute risk aversions, using an exponential function Ŵ i ≦W≦Ŵ i+1 , u i (W)=a i −b i exp(−α i W i ), where Ŵ i , i=1, . . . , K, are discrete wealth levels representing the borders of each piece i such that below each Ŵ i the risk aversion is α i and above Ŵ i to Ŵ 1+1 the risk aversion is α i+1 for all i=1, . . . , K, the coefficients of the pieces i being identified by matching function values and first derivatives at intersections Ŵ i , where the first derivative with respect to wealth is u 1 ′(W i )=b i α i exp(−α i W i ) and at each wealth level Ŵ i the risk aversions α i and α i+1 are obtained as the solution to the following two equations: a i −b i e −α i Ŵ i =a i+1 −b i+1 e −α i+1 Ŵ i b i α i e −α i Ŵ i +b i+1 α i+1 e −α i+1 Ŵ i from which the coefficients a i+1 and b i+1 are calculated as b i + 1 = b i ⁢ α i α i + 1 ⁢ ⅇ ( α i + 1 - α 1 ) ⁢ W ^ i a i + 1 = a i - b i ⁡ ( 1 - α i α i + 1 ) ⁢ e - α i ⁢ W ^ i , where a 1 =0 and b 1 =1 and the piecewise exponential function spans a range of attainable wealth levels ranging between Ŵ 1 to Ŵ 1+1 ; computing a i+1 and b 1+1 for each i=1, . . . , K starting from a 1 =0 and b 1 =1 and given the computed risk aversions α i by one or more computers; outputting risk aversion versus wealth by one or more computers to directly provide an accurate representation for an entire monetary range applicable to the investor; and determining asset allocation by one or more computers, using the given investor risk level by matching the given investor risk level to the outputted risk aversion to provide the corresponding outputted attainable wealth level.