Computation, The Missing Ingredient in Classical Economics Edward Tsang Centre for Computational Finance and Economic Agents (CCFEA) University of Essex

Classical Economics To model economic relations (often mathematically) Start with assumptions Results follow Robust… … as long as the assumptions hold…

Assumptions in Classical Economics Computation is taken for granted! The Perfect Rationality Assumption – Everyone can find the optimal solution The Homogeneity Assumption – Everyone can find solutions as good as others (quality) – Everyone takes more or less the same amount of time to find solutions (speed)

“Neither can live while the other survives” If the homogeneity assumption holds… – much of computer science is not worth studying – much of computational intelligence is irrelevant Quote from J K Rowling, “Harry Potter: The Order of Phoenix“, 2003

What is rationality? What happens when computation is involved?

Which Option Will You Take?

£100 now … £10 per month for 12 months or

What Is Your Move? What is the optimal move? Rules are clearly defined No hidden information Shouldn’t a rational player pick the optimal move? Problem: combinatorial explosion! – Too much to compute!

Computational Intelligence in Game Theory

Bargaining in Game Theory Player 1Player 2

Classical approach to Bargaining Assume Perfect Rationality Player 1 asks: – What would he offer should he reject my offer? Solve this subgame recursively… Work out the subgames to infinity, then Player 1 knows what to offer Problems: – Slight alterations to problem  Laborious study – Solutions absent for slightly complex problems !! Question: Is this a realistic solution?

“If I were the queen of France, I shall give you 1 million Euro” “If you give me a fish, I shall sing you a song”

Evolutionary Computation in Bargaining Our approach: use co-evolution to approximate subgame equilibrium Advantages: – Capable of handling complex models – Easy to modify Assumption: replace Perfect Rationality by Reinforcement Learning Population 1 Modelling player 1 Population 1 Modelling player 1 Play against each other through Co-evolution

Modelling, Simulation and Machine Learning

Agent-based Computational Economics 4. Modify models in attempt to achieve desirable behaviour Market (e.g. credit card) Agent 1 Agent 2 Agent n 2. Simulate interactions 3. Observe results 1. Model agents & market Through Machine Learning Automate the cycle

Computational Intelligence in Portfolio Optimization

Classical Portfolio Optimization Investment basics: – Maximize return, minimize risk Principle: Diversification reduces risk without compromising return Given: a set of assets (S1, S2, …, Sn) Task: decide investments, e.g. (7%, 8%, …, 2%) Assumptions in Markowitz model: – No constraint on how much to buy which asset

Efficient Frontier Fix risk Max return? Multi-objective optimization The frontier is never smooth in reality!

Approximation in Modeling or Solution? How to pick the optimal portfolio? Markowitz’s simplified model… … which enables optimal solution Build realistic models… … for which one can only find approximations Closer approximation Remote approximation Modeling: Financial Expertise required Finding solutions: Computation Expertise required +

So far… Bargaining: – reinforcement learning is a more realistic assumption than perfect rationality Modeling: – Machine learning could build better models faster Portfolio optimization: – Model  more realistic, optimization  harder – 2-objectives problem Economists must face the reality…

Computation Decision Is Complex Maximize profit P− C Finding the optimal solution demands a computational cost C Increasing C improves P (E.g. by employing CI experts) How much C improves P by how much? Unclear when one starts! Sometimes P is time- dependent! Hence… The computational decision is non-trivial!

Conclusions Classical economics took computation for granted The reality is: – Finding optimal solution is often impossible – Some can find better solutions than others – Some can find better solutions faster than others Computational Intelligence has major roles to play in economics and finance!