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Optimizing Multi-Period DFA Systems

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

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Optimizing Multi-Period DFA Systems

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

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

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

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

  5. 1 2 3 4 ... T time Horizon Purpose of a Scenario Generator • Construct a representative set of scenarios: plausible paths over planning period – S • Economic factors • Asset returns • Liabilities • Business activities • Use in financial simulator and optimizer

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

  7. Employ stochastic processes for key economic factors: interest rates inflation currencies 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 Generating Scenarios scenarios

  8. Model Uncertainties Simulate Organization scenarios Calibrate and sample Optimize

  9. 1 2 3 4 ... T time Horizon Corporate Simulations • Project state of company across multi-year horizon • Decisions at beginning each stage • Uncertainties during periods • Policy rules guide system • Iterate over all scenarios Decisions Examples: American Re, Renaissance Re, Tillinghast TAS-PC

  10. 1 2 3 4 ... T time Horizon Basic Constructs Asset allocation Also decisions regarding corporate structure

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

  12. Model Uncertainties Simulate Organization scenarios Calibrate and sample Optimize

  13. Optimization Framework • Surplust = market value (assetst - liabilitiest) • 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} • Policy constraints, plus risk measures, e.g. sufficient capital to meet 100-200 year losses

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

  15. Stochastic Programs Xj,ts 1 2 3 time

  16. Structure of Multi-stage Models A1 A2 A = scenarios As Non-anticipativity constraints

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

  18. Non-Convexity Asset/Liability Efficient Frontier 50 Year Time Horizon 9.0 10 8.5 9 8 8.0 Payout On 7 Average Compound Portfolio Return Current 6 7.5 5 4 7.0 3 2 1 6.5 2.22 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38 2.40 2.42

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

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