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Which [type of] Mathematics for Financial Resilience?

@. Which [type of] Mathematics for Financial Resilience? . IMA Conference on Mathematics in Finance Heriot-Watt Edinburgh 8 th Apr ‘ 13. Dr DJ Marsay C.Math FIMA Senior Researcher, ISRS. Preview.

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Which [type of] Mathematics for Financial Resilience?

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  1. @ Which [type of] Mathematicsfor Financial Resilience? IMA Conference on Mathematics in Finance Heriot-Watt Edinburgh 8th Apr ‘13 Dr DJ Marsay C.Math FIMA Senior Researcher, ISRS

  2. Preview • I am a boffin, interested in the actual and potential role of mathematicsin connection with crises. • This talk considers finance, linked to Cabinet Office thinking to illustratethe kind of thing that is needed.

  3. Finance “Anyone who believes exponential growth can go on forever in a finite world is eithera madman or an economist.” Attrib, Kenneth Boulding, Evolutionary economist, 1973 “[T]he financial crisis has shown that … there are serious dangers if fancy mathematical tools are used by people who do not understand their limitations.” David Spiegelhalter,Mathematics Today, Aug 2012

  4. Mathematics • Mathematics is not only about: • efficient computational models / algorithms • but also • challenging ‘given’ theories.

  5. Crises (de-regulation) Useful debates, largely forgotten Big-Bang happened 2008 crash! Due to Big Bang? End of Cold War! Big-Bang? opportunity risk Y2k crash:useful organisational changes Recovery! has not happened A subjective view

  6. Aspiration To recognize and work within the limits of our mathematics, and to expand them. Preferably, mathematics that: Supports immediate, recognized ‘wants’. Can be used to address longer-term issues. Is meaningful to clients (e.g. policy-makers). Lacks misleading ‘baggage’. But where to start?

  7. The Ratio Club Donald MacKay, for Ratio Club, 1952 Turing, Good, Ashby et al. Consistent with Whitehead and Russell. Even Gordon Brown knows who Turing is.

  8. Turing’s Morphogenesis • Turing considers a model of potential instability:∂tq= Dq + R(q),where q is a vector of properties, D is a diagonal diffusion matrix and is a (local) reaction. • Without diffusion one has a single epoch with regular oscillations. • Moderate diffusion leads to a variety of ‘emergent behaviours’, with greater impact near critical instabilities, whereis degenerate. • One does not always get a new stable epoch: one can get ‘wandering’ behaviour near critical instabilities.

  9. Morphogenesis with Momentum • Turing’s application was to the development of form in biology, which tends to stabilise. • The theory can also be applied to processes, such as evolution, which do not stabilise. • Crises are symptomatic of instability, which is associated with momentum. • We can model this using 2 variables, or equivalently as.

  10. Correspondence The theory can be judged, not by its ability to predict values q(t) (which it claims to be impossible), but by the correspondence of scenarios and behaviours: Diffusion Reaction Inertia Conditions Morphogenesis Experience Critical instabilities Emergent properties ‘Wandering’ Behaviours? Aim to fit the long-term ‘big picture’, not the short-run fine detail.

  11. , q-q3 • With the same initial conditions, one gets a variety of temporary oscillations, plus some ‘wandering’ behaviours. • Diffusion may happen to reduce or increase variability. • Transitions are most likely near the critical instabilities (0, i.e. near q=0,1). q time 

  12. Reasoning through instabilities • For common stochastic systems, one can form ‘rational expectations’ by extrapolating the probable behaviour without diffusion and adding variability:q(D,t) q(D=0,t) + σ(D,t) • But uncertainty concerning instabilities is not comparable with variability. • So conventional probabilistic reasoning is not appropriate. • Can you extrapolate from a caterpillar to a butterfly? • Or do you need ‘scenario analysis’?

  13. Reasoning through instabilities • Turing developed, with Jack Good, a notion of ‘weight of evidence’, with a formulaW( E | H : C ) s { s( W( Es | H : C ) )},for a hypothesis H, a context C, total evidence, E, consisting of evidences Es from sources s, and where each s( ) is a discountingfunction, depending on confounding factors. • For precise hypotheses, not discounting, with a little manipulation, yields Bayes’ rule:P(H|E)=P(E|H).(P(H)/P(E)),and hence conventional probabilistic reasoning. • But are we justified in making these assumptions? Or can there be emergence?

  14. Crises • Diffusion, reactionand momentum are present • Loss of confidence and panic can spread quickly. • Crises are almost defined by critical instabilities. • Actions have most impact near critical instabilities. • Experience and models from before an instability can be very misleading (‘reversed levers’). • Outcomes seem emergent, unless bold action eliminates the instabilities. • But exogenous changes in expectation and policy can distort and complicate the picture.

  15. Inspired by analysis for conflict resolution. ‘Synthetic Modelling of Uncertain Temporal Systems’, based on Smuts’ theory of emergence. An ‘Exploratorium’ • Shows emergence, uncertainty, entropy, ‘abstract indicators’. • Informed UK crisis management. Various UK and Allied Defence and Security presentations 1999-2010

  16. An emergent new definite context is not inevitable … Collaborative Working document, 2007 and may not be desirable. zone 1 2 3 4 5 placid random turbulent “swimming with the fishes” • internal adjustment • independent activity • closed models • adaptation at all levels • coherent activity • open appreciation ? Implications for collaboration

  17. Finance and Economics • Indicators of criticality: • Developments (economic, industrial, urban) seem emergent where no one factor dominates. • Markets are more prone to crises where speculation (momentum / impulse ) is more significant than fundamentals (reaction / propagation). • Conventional methods of analysis and prediction seem unusually unreliable. • Implications: • We should recognise that conventional methods are limited to non-critical cases. • It may be our assumptions that turn emergence into disaster.

  18. The Nexus, 2008 To US, UK and PRC, for example, the issues seemed very different. But they were not just using different models, but were concerned with different types of uncertainty and implicit time-frames. We need help to situate these different views.

  19. Levels • Epoch horizons can be based on Turing: • Short: Until the next instability. • Medium: Until the next instability whose potential is not adequately understood. • Long: Seeking to work through instabilities with uncertain potential behaviours. • But further aids seem needed.

  20. uncertain Effectiveness /Uncertaintyproblem ambiguous probabilistic Efficiency / overloadproblem High data volumefor time available Low data volume,human pace Locating the key finance issues? Different Mathematics? No requirement Most Applications of Mathematics Current capability factual Adapted from IMA ‘Mathematics in Defence 2009’

  21. Risks become apparent. Energy Extrapolation appears to work, but hidden risks are building. B New context emerges,. Incoherence Extrapolation ‘works’ C A’ Extrapolation becoming effective. A Time Typical crisis kinematics Dynamics of Financial Issues + What are the limitations of conventional methods? Where will any new context come from? Will it be favourable? Are Bubbles a good metaphor?Baggage? Adapted from IMA ‘Mathematics in Defence 2009’

  22. What happened? No ‘negative bubble effect’. Fits Turing et al. But could change of government been a factor? Or EU? … Source: Thomson Reuters Simple linear trend used for pre-crisis trends

  23. ACab.Off. Perspective Outline Clear links to mathematical issues? Evolutionary fitness: The concept of Resilience to Crises Evolutionary patterns: Learning the lessons of history? Shock, surprise & irresilience:Managing neutered risk is not enough Evolving strategies:Real options for gaining traction in time

  24. ENDS COUNTER-MEASURE ASSESSMENT Information Requirements Information Requirements Cost Benefit Cost & Criticality Probable & Expected Value Loss IMPACT ASSESSMENT VULNERABILITY THREAT Weakness Exploitation Exposure Capability Intent Opportunity What & Which Who & How Where & When What & Which Who & How Where & When MEANS A C.O. Perspective, 1999 -- Conventional risk analysis POLICY Contingencies Mathematically, This seems to assume a single epoch. Atomised control freakery left, right & centre

  25. ACab.Off. Perspective, 1999 -- Thwarting peacetime transformation Value? EXPLORE Epochs? • Diversity • Select & Grow • Variable Durations Interactive Knowledge Blend of Investments(BoI) &(RoI) Return on Investments Exploitation squeezes out Exploration Learning Myopia EXPLOIT • Fixed timescales • Niche specialists • Reward narrowRational behaviour Yield

  26. Resilience Issues • Crises have their own imperatives. • Our mathematics and scientific approach should not get in the way, and ideally should help. • As a minimum, we need to appreciate our limitations.

  27. Resilience Issues? • If Whitehead, Turing et. al. are right, resilience also relies on: • Identifying critical instabilities. • Appreciating which data and judgements to trust or discount, when. • Recognition that the ‘mechanism’ can change. • And, ideally, on reasoning through instabilities: • Reformed concepts of uncertainty, value etc. • Appreciating the nature of crises and of uncertainty as well as normal domain expertise. • E.g., by recognizing or creating an extra dimension.

  28. Financial ‘prediction’ • Critical instabilities matter in the medium-term • There may be no ‘regression to the mean’. Source: Bank of England Inflation Reports, 2/07. Rescaled to match 3/13. • Volatility, ‘tail-risk’ and fan-charts are only meaningful in the short-term. Source: Bank of England Inflation Reports, 3/13.

  29. Towards Sustainable Recovery? • Estimation of ‘the multiplier’ (growth/cuts) • Discount evidence before 2009 (different epoch). • Look at which other country’s data? (‘Frame’) • Is there potential to transform the economy? • Could Brown’s Green agenda have transformed? • Is there scope for initiatives around inequality?(E.g. German-style boards.) • What scope for regulation? • E.g. should the government promote understanding of speculation and crises? Would this be enough?

  30. Conclusions • Mainstream financial and economic mathematics have myopically focussed on ‘exploit’. To inform policy, they need to address ‘explore’ as well. • The mathematical framework of Turing et al provides a good ‘seed’, with worked examples. • ‘Understanding limitations’ would be a good start. • Developing a reformed concept of ‘value’ might be a good aspiration. • But the issues are broader than just finance.

  31. @ Which type of Mathematicsfor Financial Resilience? Comments & Questions? IMA Conference on Mathematics in Finance Heriot-Watt Edinburgh 8th Apr ’13 Dr DJ Marsay C. Math FIMA Senior Researcher, ISRS djmarsay@ucl.ac.uk, djmarsay.wordpress.com, LinkedIn.

  32. A general ontological approach (1979) Graphic from Peter Allen, Cranfield Taking Whitehead and Russell seriously. Normal approaches are only valid in stable ‘epochs’. This limitation is no longer so appreciated.

  33. Empirical Support: Conflict Deaths 1945 - 2005 PerestroikaGlasnost Clear epochs, with ‘crisis’ in late 80s. Consistent with Turing et al.

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