Comparing adaptive management and real options approaches: slides and pre-print

A comparison of adaptive management and real options approaches for environmental decision makingiadine Chadès, T. Tarnopolskaya, S. Dunstall, J. Rhodes, and A. Tulloch http://iadine-chades.org/@iadinec

There are many things we don’t know: uncertainty.Urgency and planning: decide today but think about tomorrow.Don’t spend too much! We want our decisions to achieve something and do it well.

Making decisions is difficult. Why?

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statet statet+1 statet+2

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How do we know if we are making good decisions?We need 1) an objective 2) to assess (monitor) whether our decisions are getting us closer to our objective.

Good?Bad?

Good?Bad?

Adaptive management (AM) & real options (RO)

Both approaches are based on stochastic optimal control and Markov decision processes.

AM accounts for a small number of hidden variables. RO deals with high-dimensional problems with multiple stochastic risk factors.


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Good?Bad?

Good?Bad?

Adaptive Management is ‘learning by doing’Adaptive management is an iterative process of reducing uncertainty through time by learning by doing and monitoring (Walters and Hilborn, 1978).Principal tool for conserving endangered species under global change.

CSIRO. POMDP the Swiss army knife of the adaptive ecologist

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Don’t knowt+1Don’t knowt

Adaptive management is “learning by doing”


Decisions are selected to achieve a management objective while simultaneously gaining information to improve future management outcomes.

manage

monitor

learn

objective

Specifically tailored to account for structural uncertainty:1) Parameter: survival,

growth, probability of success

2) Model: competing scenarios, density dependence

Adaptive management is making decisions when we don’t know the system dynamics


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R. Bellman

Stochastic dynamic programmingmanage

monitor

learn

objective

Bayes theorem

Active adaptive management calculates a plan that provides the best actions to implement, given our current knowledge … and what we will learn in the future


R. Bellman

Stochastic dynamic programmingmanage

monitor

learn

objective

Bayes theorem

Passive adaptive management calculates a plan that provides the best actions to implement, given our current knowledge … Learning occurs independently.

Two types of adaptive management principle: active and passive


Active: Includes future learning opportunities when calculating best decisions. Solutions are optimal, but difficult to calculate! Active AM = POMDP (Chades et al, AAAI 2012)

Passive: Heuristics approaches developed because finding the

optimal solution might be impossible. Assumes “certainty equivalence”. No formal guarantee of

performance.Techniques: Stochastic Dynamic Programming (MDP)

Where and when should we invest in sea level rise mitigation to protect migratory shorebirds under uncertainty?

2) Adaptive management (Nicol et al, 2013, IJCAI) (Nicol et al, Proc B 2015).Learn as we manage:

birds saved +56.2%

1) Bottleneck index (Iwamura et al, 2013, Proc. B)

birds saved +31%

Uncertain future SLR scenarios and consequences

Where and when to protect?

East Asian Australasian flyway

Real Options Concept

Flexibility to adapt to changing circumstances is crucial for successful business operation under uncertainty

Uncertainty creates opportunity which can be harnessed, using project’s flexibility, to improve project’s performance

Concept came from financial risk areaReal option: right (without obligation) to undertake a certain business activity in the future

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Dual purpose of Real Options

Real Options Valuation / Analysis:

1. Dynamic project valuation under uncertainty. 2. Flexible management under uncertainty

(optimisation of sequential decisions under uncertainty)

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Real Options Value vs NPVValue of flexibility

Net Present Value (NPV) – a static, passive project valuation approach. It assumes that decisions are taken today and will not be changed

Real Options Valuation is based on optimising both decisions (options) and their timing in the future under uncertainty

Optimal flexible management in the face of uncertainty adds value

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Value of flexibility

Project value NPV Option Value

Examples of Real Options

to delay, temporarily stop or completely abandon the project in the future

to expand or contract the project in the future to accelerate/decelerate the project in the futureA decision to stop timber harvesting when a woodland caribou population becomes threatened with extinction (Morgan et al., 2007)Current applications of real options typically consider a single real

option under a single stochastic risk factor. Do not require advanced numerical techniques.

Future applications for adapting to climate change: broader range of stochastic processes and new techniques (Mezey and Conrad, 2010)

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Regression Monte Carlo ApproachRegression Monte Carlo: a combination of Monte Carlo simulations with Bellman Optimality Principle (Stochastic dynamic programming)

Introduced in the finance industry by Longstaff & Schwarz (2001) under the name Least Squares Monte Carlo (LSMC).

LSMC has drawbacks (stability problems, memory complexity) that prevent its use for high-dimensional problems:

New advanced regression Monte Carlo methods are suitable for complex high-dimensional real options problems:

New regression Monte Carlo Methods for high-dimensional real options problems in minerals industry, by Langrene, Tarnopolskaya, Chen, Zhu and Cooksey – MODSIM2015, Session E6 Real Options

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Adaptive Management Real OptionsAttitude to uncertainty

Reduce structural uncertainty to maximise management outcomes.

Harness uncertainty to add value though optimal management.





Mathematical model

Markov property, MDP or POMDP with state space augmented with sufficient statistics. Probability transitions pre-calculated (not simulated).

Markov property, optimal stopping and optimal stochastic switching (MDP). Solved using regression Monte Carlo approach (simulation based).





Mathematical model



Role of learning

Learning is part of the decision process

Real options analysis share similarities with passive adaptive management





Mathematical model



Role of learning



Purpose Optimal management through learning

Capital budgeting and optimal flexible management





Mathematical model



Role of learning





Features of advanced methods

Small number of risk factors; non stationary dynamics; large states space; small action space; imperfect detection.

Multiple stochastic risk factors; non stationary dynamics; large state and action space





Mathematical model



Role of learning





Features of advanced methods

Small number of risk factors; non stationary dynamics; large states space; small action space; imperfect detection.

Multiple stochastic risk factors; non stationary dynamics; large state and action space

Problem size 800,000 discrete states, less than 10 actions, 1 hidden stochastic risk factor and infinite time horizon

Continuous state space sampled via Monte Carlo simu (up to 1,000,000 realizations), up to 50 actions; up to 10 stochastic risk factors; long time horizons

Thank youDr Iadine Chadèse [email protected]

http://iadine-chades.org/Twitter: @iadinec

Thanks to all my collaborators

This work has been supported by a Julius Career award (I.C.)

Science

Comparing adaptive management and real options approaches: slides and pre-print