1. Dynamic asset and liability management

2. Financial Optimization and Risk Management Professor Alexei A. Gaivoronski Asset and Liability Management (ALM) Scenario tree At each date manager assesses new information about prices, volatilities, interest rates … and take portfolio rebalancing decision Borrowing, liabilities

3. Financial Optimization and Risk Management Professor Alexei A. Gaivoronski Asset and Liability Management (ALM) Sequence of investment decisions First stage (t=0)  Prices and portfolio composition are known  Inventory balance constraint:  Cashflow balance constraint Asset endowment after rebalancing Initial asset endowment Asset bought Asset sold Value sold Initial asset value Liabilities value Borrowed value Value bought Value invested short term

4. Financial Optimization and Risk Management Professor Alexei A. Gaivoronski Asset and Liability Management (ALM) Trading date t  Cashflow balance

5. Financial Optimization and Risk Management Professor Alexei A. Gaivoronski Asset and Liability Management (ALM) Trading date t  Inventory balance

6. Financial Optimization and Risk Management Professor Alexei A. Gaivoronski Asset and Liability Management (ALM) Trading date t  Inventory balance constraint  Cash flow constraint  End of horizon constraint  Different other constraints: regulatory, etc.

7. Financial Optimization and Risk Management Professor Alexei A. Gaivoronski Asset and Liability Management (ALM) Objective: maximize utility of terminal wealth  Other objectives depend on particular setting (deviation fom target index, etc.) Resulting model