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Dynamic Decision Making when Risk Perception depends on Past Experience. Michèle COHEN, CES, Université de Paris 1 Johanna ETNER, GAINS, Univ. du Maine et CES, Paris 1 Meglena JELEVA, GAINS, Univ. du Maine et CES, Paris 1. Introduction Behavior at a point of time Dynamic choice

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dynamic decision making when risk perception depends on past experience

Dynamic Decision Making when Risk Perception depends on Past Experience

Michèle COHEN, CES, Université de Paris 1

Johanna ETNER, GAINS, Univ. du Maine et CES, Paris 1

Meglena JELEVA, GAINS, Univ. du Maine et CES, Paris 1

slide2
Introduction
  • Behavior at a point of time
  • Dynamic choice
  • An illustrative example: past experience and insurance demand

FUR XII, Rome 2006

1 introduction 1 3
1. Introduction (1/3)
  • Risk and wealth perception may be influenced by the agent context when he takes his decisions
  • Context = framing, past experience, feelings etc.
  • In this paper: focus on past experience
  • Some empirical evidence:
    • Relation between insurance decisions and individual prior-experience related to risk:
      • Kunreuther (1996), Brown, Hoyt (2000);
    • Weather conditions influence investment decisions:
      • Hirshleifer, Shumway (2003)

FUR XII, Rome 2006

1 introduction 2 3
1. Introduction (2/3)
  • Past experience can concern different events:
    • Past realizations on the decision-relevant events (accidents);
    • Realizations of events, independant on the relevant decision problem (weather).
  • To better capture the long term impact of past experience, we model intertemporal decisions.
  • A first step consists in considering a one period decision problem where preferences are defined on pairs (decision, past experience);

FUR XII, Rome 2006

1 introduction 3 3
1. Introduction (3/3)
  • We adapt RDU axiomatic system of Chateauneuf (1999);
  • The obtained criterion is used in the construction of a dynamic choice model under risk;
  • We model intertemporal decisions by a recursive model à la Kreps, Porteus (1978).

FUR XII, Rome 2006

2 behavior at a point of time 1 4
2. Behavior at a point of time (1/4)
  • Decision problem characterized by:
    • L: set of lotteries over Z  R;
    • S: set of past (realized) states;
    • (s , L): « past experience dependent lottery »;
  • : preference relation on S  L.

FUR XII, Rome 2006

2 behavior at a point of time 2 4
2. Behavior at a point of time (2/4)
  • Preferences representation on S  L in 3 steps:
    • for any fixed s, s on s  L, from Chateauneuf (1999):
    • S  Z on S  Z, axioms to guarantee the existence of a utility function on S  Z.
    • Additional axioms to guarantee the consistency of the conditional preference relations.

FUR XII, Rome 2006

2 behavior at a point of time 3 4
2. Behavior at a point of time (3/4)
  • Theorem on S L is representable by a function V:

FUR XII, Rome 2006

2 behavior at a point of time 4 4
2. Behavior at a point of time (4/4)
  • Some particular cases:
    • Realized states influence only the probability transformation function:
    • Realized states influence only the utility function:

FUR XII, Rome 2006

3 dynamic choice 1 5
3. Dynamic choice (1/5)
  • In the spirit of Kreps, Porteus modelling
  • Some notations and assumptions:
    • T periods;
    • Zt = Z  R;
    • Past experience at time t: st = (e0, e1,…,et) with et Et;
    • St : set of possible past experiences up to time t such that:

S0 = E0 and St = St-1  Et;

    • M(Et): set of distributions on Et.

FUR XII, Rome 2006

3 dynamic choice 2 5
3. Dynamic choice (2/5)
  • At period T,
    • LT: set of distributions on ZT ;
    • XT: set of closed non empty subsets of LT.
  • Recursively,
    • Lt: set of probability distributions on

Ct = Zt Xt+1M(Et+1), with Xt+1 the set of closed non empty subsets of Lt+1.

FUR XII, Rome 2006

3 dynamic choice 3 5
3. Dynamic choice (3/5)
  • For the same period, assumption of compound lotteries reduction (ROCL) is made between distributions of wealth and events.
  • Between two consecutive periods, ROCL remains relaxed.

FUR XII, Rome 2006

3 dynamic choice 4 5
3. Dynamic choice (4/5)
  • For each period t, t on st Lt, for a given st represented by:
  • Temporal consistency axiom

For any t, s t, et+1,zt, xt+1, x’t+1,

FUR XII, Rome 2006

3 dynamic choice 5 5
3. Dynamic choice (5/5)
  • Representation theorem

There exist 2 sequences of utilities ut and vt and a sequence of t such that:

FUR XII, Rome 2006

4 an illustrative exemple 1 4
4. An illustrative exemple (1/4)
  • Insurance demand
    • An individual faces a risk of loss and has to choose an amount of insurance coverage,  ;
    • Insurance contracts are subscribed for one period (year)
    • Risk characteristics:
      • loss of an amount L with probability p;
      • P(loss in period t/ loss in period t-1) = p

FUR XII, Rome 2006

4 an illustrative exemple 2 4
4. An illustrative exemple (2/4)
  • Optimal insurance strategy of an individual for 3 periods of time?
  • Insurance contracts: subscibed for 1 year, fair premium
  • Past experience at t:

sequence of loss realizations before t

et= e if « loss at period t », et= e’ if « no loss at period t »

st = (st-1, et)

FUR XII, Rome 2006

slide17

L3

z3

a3

z2

p

1-p

z3

z1

L2

a2

s2=(e0,e1,e2)

p

z’3

z2

L’3

a’3

p

s1=(e0,e1)

1-p

1-p

z’3

s’2=(e0,e1,e’2)

L1

z0

a1

p

z’’3

z’2

L’’3

s0=e0

a’’3

p

1-p

L’2

s’’2=(e0,e’1,e2)

1-p

z’’3

z1

a’2

z’’’3

p

z’2

L’’’3

s’1=(e0,e’1)

a’’’3

1-p

s’’’2=(e0,e’1,e’2)

z’’’3

1-p

4. An illustrative exemple (3/4)

p

FUR XII, Rome 2006

4 an illustrative exemple 4 4
4. An illustrative exemple (4/4)
  • Let
  • Results:
    • 1 = 0;
    • 2 = 0 if no loss at period 1;

2 [0, 1] if loss at period 1;

    • 3 = 0 if no loss at periods 1 and 2;

3 = 1 if loss at periods 1 and 2;

3 [0, 1] else.

FUR XII, Rome 2006