2020  OriginalPaper  Chapter
5. Designing Insurance Against Extreme Weather Risk: The Case of HuRLOs
Authors: Martin Boyer, Michèle Breton, Pascal François
Publisher: Springer International Publishing
2020  OriginalPaper  Chapter
Authors: Martin Boyer, Michèle Breton, Pascal François
Publisher: Springer International Publishing
Notation

Definition


K

Number of counties, indexed by
k ∈ {1,…,
K}.

I

Number of players, indexed by
i ∈ {1,…,
I}.

J

Index of the option series,
j ∈ {1, 2, 3}.

W
_{i}

Current wealth of player,
i ∈ {1,…,
I}.

p
_{k}

Conditional probability that a hurricane present in the Atlantic Basin will make landfall in county
k. For
k = 0,
p
_{0} = 1−∑
_{k}
p
_{k} is the probability that it will not make landfall.

L
_{ik}

Potential (expected) losses of player
i in county
k, where
L
_{i0} ≡ 0.

c

Nominal value of a HuRLO.

R
_{jk}

Payoff of an option
k in series
j if outcome
k is realized.

O
_{jk}

Decimal odds of outcome
k in series
j.

q
_{jk}

Implied market probabilities for outcome
k in series
j.

P
_{jk}

Probability that option
k of series
j will mature inthemoney.

n
_{ijk}

Number of each option
k of series
j owned by player
i.

m
_{jk}

Number of each option
k of series
j in the market.

M
_{j}

Total mutual reserve of series
j.

π
_{jk}

Market price of option
k of series
j.

Y
_{i}

Expected utility of agent
i.

γ

Risk aversion parameter.

r

Annual discount rate.

d

Time remaining until the end of the hurricane season.

H

Number of series that have already been executed.

l

Indicator of the presence of a hurricane.

λ

Annual expected number of hurricanes.

Region

Year start

Number of years

Coastline (km)

Number of storms to make landfall

Probability of at least 1 storm making landfall in the region in a given year

Probability of no storm making landfall in the region over a 10 year horizon



Named

Hurricanes

Intense hurricanes

Named (%)

Hurricanes (%)

Intense hurricanes (%)

Named (%)

Hurricanes (%)

Intense hurricanes (%)


1

1880

136

503

72

43

17

43

27

12

0

4

29

2

1880

136

257

27

13

4

19

9

3

12

38

75

3

1880

136

666

104

51

23

56

31

16

0

2

18

4

1880

136

382

44

19

2

29

13

1

3

25

86

5

1900

116

373

26

9

5

22

7

4

9

46

65

6

1900

116

483

49

35

16

37

26

13

1

5

25

7

1880

136

574

25

11

3

18

8

2

14

45

80

8

1851

165

673

83

54

15

41

28

9

0

4

40

9

1851

165

527

14

5

0

9

3

0

41

74

100

10

1851

165

426

26

15

7

15

9

4

19

40

65

11

1851

165

447

9

5

0

6

3

0

56

74

100
