Optimizing Multi-Period DFA Systems Professor John M. Mulvey Department of OR and Financial Engineering Bendheim Center for Finance Princeton University July 2000

Strategic Asset and Liability Systems (DFA) Towers Perrin-Tillinghast CAP:Link/OPT:Link, TAS F significant impact (e.g. US West -- $450 to 1001 Million) u American/Munich Re-Insurance – ARMS u Financial planning for individuals –Home Account, Financial Engines u KontraG bill in Germany u W. Ziemba and J. Mulvey, eds., World Wide Asset and Liability Modeling, Cambridge University Press, 1998 Single models

Limitations of Traditional Mean- Variance u Single period –Transaction and market impact costs –Cannot compare short-term and long-term u Ignores liabilities –Misses contribution patterns –Risks are asset-only u Assumes symmetric returns

Model Uncertainties Simulate Organization scenarios Risk aversion Calibrate and sample What ifs Basic Technology Optimize

Purpose of a Scenario Generator u Construct a representative set of scenarios: plausible paths over planning period – S –Economic factors –Asset returns –Liabilities –Business activities u Use in financial simulator and optimizer T time Horizon

Structural models are well placed to support DFA Company Strategy Asset Mix Product Mix Capital Structure Reinsurance Economic Scenario Generator Projected Financials Risk Profile = Distribution of Future Financial Results Asset Behavior Model Product Behavior Model Noise Optimization Inflation Interest Rates Credit Costs Currency Exchange GDP

Generating Scenarios u Employ stochastic processes for key economic factors: –interest rates –inflation –currencies u Sample with discrete time and discrete scenarios Examples: Towers Perrin’s global CAP:Link (Tillinghast TAS) Calibrated in 21 countries Siemens Financial Services Tree generator

Model Uncertainties Simulate Organization scenarios Calibrate and sample Optimize

Corporate Simulations u Project state of company across multi-year horizon –Decisions at beginning each stage –Uncertainties during periods –Policy rules guide system –Iterate over all scenarios T time Horizon Decisions Examples: American Re, Renaissance Re, Tillinghast TAS-PC

Basic Constructs T time Horizon Also decisions regarding corporate structure Asset allocation

Investment Network with Borrowing (each scenario) Contribution and pay pension benefits

Model Uncertainties Simulate Organization scenarios Calibrate and sample Optimize

Optimization Framework u Surplus t = market value (assets t - liabilities t ) u Grow economic surplus over planning period, pay liabilities, reduce insurance costs –t = {1, 2, …, T} –maximize risk-adjusted profit –analyze over representative set of scenarios {S} u Policy constraints, plus risk measures, e.g. sufficient capital to meet year losses

Dynamic Optimization Approaches u Dynamic stochastic control (Brennan-Schwartz-Lagnado) F relatively simple stochastic model F small state-space, few general constraints u Multi-stage stochastic programming (Frank Russell) F realistic decision framework, sample scenarios F large-size due to # conditional variables u Optimize decision rules ( Towers Perrin/Tillinghast ) F understandable, generate confidence estimates F non-convex

Stochastic Programs 123 time X j,t s

Structure of Multi-stage Models A1A1 A2A2 AsAs Non-anticipativity constraints scenarios

Optimize over Policy u Decision rules satisfy non-anticipativity conditions u Example -- surplus management strategy -- Goals-at- Risk TM u Intuitive, easy to implement u Generates small, highly non-convex optimization problem u Employ stochastic program to inspire good decision rules

Non-Convexity Asset/Liability Efficient Frontier 50 Year Time Horizon Average Compound Portfolio Return Payout On Current

Conclusions u Multi-period DFA systems are operating today –Better linkages needed with tactical systems u Customized products will grow from integrated risk management systems u Implementation in various applications –Pension planning –Insurance companies –Coordinated risk management for divisions –Individuals