SCOP: Schrodinger Control Optimal Planning for Goal-Based Wealth Management

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What is the main result of the paper?

AI: The main result of the paper is the development of a semi-analytical approach to solve the optimization problem of contributions to a financial plan for retirement. The authors suggest a method based on solving controlled Schrödinger equations and reducing the problem to a representation of efficient frontiers. They provide solutions for the Schrödinger equations and demonstrate the use of efficient frontiers for policy optimization.

Who is the author of the paper?

AI: Based on the answers provided before, the author of the paper is not mentioned in the provided information.


Igor Halperin


We consider the problem of optimization of contributions of a financial planner such as a working individual towards a financial goal such as retirement. The objective of the planner is to find an optimal and feasible schedule of periodic installments to an investment portfolio set up towards the goal. Because portfolio returns are random, the practical version of the problem amounts to finding an optimal contribution scheme such that the goal is satisfied at a given confidence level. This paper suggests a semi-analytical approach to a continuous-time version of this problem based on a controlled backward Kolmogorov equation (BKE) which describes the tail probability of the terminal wealth given a contribution policy. The controlled BKE is solved semi-analytically by reducing it to a controlled Schrodinger equation and solving the latter using an algebraic method. Numerically, our approach amounts to finding semi-analytical solutions simultaneously for all values of control parameters on a small grid, and then using the standard two-dimensional spline interpolation to simultaneously represent all satisficing solutions of the original plan optimization problem. Rather than being a point in the space of control variables, satisficing solutions form continuous contour lines (efficient frontiers) in this space.

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