Flashcards in Mango Deck (44)

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1

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CAT model outputs (2)

(Mango)

###
1. modeled loss for each event

2. probabilities of each event

2

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Cov(portfolio, new account)

(Mango)

### Cov(portfolio, new account) = sum over all events of modeled loss(portfolio) * modeled loss(new account) * probability of event * (1 - probability of event)

3

##
Combined portfolio variance, Var(portfolio + new account)

(Mango)

### Var(portfolio + new account) = Var(portfolio) + Var(new account) + 2Cov(portfolio, new account)

4

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Required surplus (V) for the marginal surplus (MS) method

(Mango)

###
V = z * S - R

where S = std. dev(loss)

and R = return

and z = # of std. deviations from the normal distribution

5

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Risk load (r) for the marginal surplus (MS) method

(Mango)

###
r = multiplier * (S(1) - S(0))

where S = std. dev(loss)

6

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Marginal surplus (MS) method description

(Mango)

### uses change in portfolio standard deviation to calculate the risk load for an account

7

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Required return (y) depends on (3)

(Mango)

###
1. mgmt goals

2. market forces

3. risk appetite

8

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Marginal variance (MV) method description

(Mango)

### uses change in portfolio variance to calculate the risk load for an account

9

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Risk load (r) for the marginal variance (MV) method

(Mango)

###
r = multiplier * marginal variance

where marginal variance = Var(new account) + 2Cov(portfolio, new account)

10

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Multiplier for the marginal variance (MV) method risk load

(Mango)

###
uses MS multiplier converted to an MV basis

multiplier = MS multiplier / std. dev(portfolio + new account)

11

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Multiplier for the marginal surplus (MS) method risk load

(Mango)

###
multiplier = [(y * z) / (1 + y)]

where y = required return

and z = # of std. deviations from the normal distribution

12

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Relationship between combined and account level risk loads under the MS and MV method (general)

(Mango)

### total portfolio risk loads are = under both methods but account level risk loads differ

13

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Build-up vs. renewal scenario

(Mango)

###
build-up = initial adding of new accounts

renewal scenario = steady state portfolio where accounts renew w/no new entrants

14

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Account renewal assumption

(Mango)

### renewing account X into portfolio Y = adding a new account X to an existing portfolio Y

15

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Marginal surplus (MS) method results under the renewal scenario & impact

(Mango)

###
sum of individual risk loads < total portfolio risk load

>> b/c of sub-additivity of the square root operator in the std. dev.

impact: undercharge every account

16

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Marginal variance (MV) method results under the renewal scenario & impact

(Mango)

###
sum of individual risk loads > total portfolio risk load

>> b/c the covariance term is double-counted (MV renewal scenario is super-additive)

impact: overcharge every account

17

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Marginal surplus (MS) and marginal variance (MV) results under the build-up scenario

(Mango)

### sum of individual risk loads = total portfolio risk load

18

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Additivity

(Mango)

###
when sum of individual risk loads = total portfolio risk load

**specifically, Mango is searching for renewal additivity

19

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Order dependency problem

(Mango)

### renewal additivity depends on the entry order of accounts

20

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Features of cooperative games with transferrable utilities under game theory (4)

(Mango)

###
1. participants have benefits/costs to share

2. opportunity to share benefits/costs from cooperation of all or a sub-group of participants

3. freedom for players to negotiate, bargain, & form coalitions

4. conflicting player objectives - each wants to maximize benefits/minimize costs

21

##
Coalition characteristic function in game theory

(Mango)

### determines the total amount to be allocated

22

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Sub-additivity and super-additivity of the coalition characteristic function, v(S)

(Mango)

###
sub-additive: v(S) + v(T) > v(S union T)

each member wants to minimize individual allocation

super-additive: v(S) + v(T) < v(S union T)

each member wants to maximize individual allocation

23

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Example of a sub-additive coalition characteristic function

(Mango)

### insurance premium for a risk purchasing group (each members wants to minimize individual premium)

24

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Game theory allocation rules to determine the optimal allocation (2)

(Mango)

###
1. allocation methods must be additive

2. coalition must be stable/fair so there is no incentive to leave the group

25

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Conditions of fairness under game theory allocation rules (2)

(Mango)

###
1. individual rationality

2. collective rationality

26

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Individual rationality

(Mango)

### players are no worse off for having joined the coalition

27

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Collective rationality

(Mango)

### no sub-group of players would be better off on its own

28

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Core of the game

(Mango)

### set of all acceptable allocations for each player satisfying fairness and stability rules

29

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Benefits of the Shapley value allocation method (3)

(Mango)

###
1. additive

2. centroid of the core

3. order independent

30