# Reduced Form Capital Optimization

## TL;DR

This paper introduces a simplified, analytically solvable model for bank capital optimization using a linear approximation of complex allocation methods, enabling optimal balance sheet and risk asset targets.

## Contribution

It presents a novel reduced form formulation of bank capital optimization based on a linear approximation of the CAS allocation, allowing analytical solutions.

## Key findings

- Provides an explicit analytical solution for optimal LBS and RWA targets.
- Demonstrates the effectiveness of the linear approximation in complex allocation scenarios.
- Facilitates more efficient capital optimization in banking.

## Abstract

We formulate banks' capital optimization problem as a classic mean variance optimization, by leveraging an accurate linear approximation to the Shapely or Constrained Aumann-Shapley (CAS) allocation of max or nested max cost functions. This reduced form formulation admits an analytical solution, to the optimal leveraged balance sheet (LBS) and risk weighted assets (RWA) target of banks' business units for achieving the best return on capital.