Download Markov Chains in Insurance Pricing and Mobile Operator Market Share and more Exercises United States History in PDF only on Docsity!
STATES E0 E
EO 1230 820
E1 990 1155
E2 1125 1575
E3 780 780
STATES E0 E
EO 0.25 0.
E1 0.28 0.
E2 0.2 0.
E3 0 0
q= 0.28 0.
Exercise 1.
XYZ insurance company charges its customers according to their accident history.
0); if you have had an accident in each of the last two years you will be charged $
(state 2) and if you had an accident the second of the last two years will be cha
accident, t
According to Table 1 by applying the Markovian processes, finding the transitio
vec
a. What is the transition matrix resulting from proportionality acc
b. What is the average premium paid by a c
0,3W+0,3X+0,25Y+0,15Z
0,2W+0,35X+0,35Y+0,15Z
p*q= 0,25W+0,15X+0,4Y+0,25Z
0,25W+0,2X+0Y+0,45Z
W+X+Y+Z
(-0,7)W+0,3X+0,25Y+0,15Z
0,2W-0,65X+0,35Y+0,15Z
p*q= 0,25W+0,15X-0,6Y+0,25Z
0,25W+0,2X+0Y-0,55Z
W+X+Y+Z-
W
X
Y
Z
W X
b.What is the average premium paid by a customer in Payoff, according t
State 0 $ 530,
State 1 $ 719,
State 2 $ 517,
State 3 $ 778,
+0,3X+0,25Y+0,15Z = W
0,35X+0,35Y+0,15Z = X
+0,15X+0,4Y+0,25Z = Y <- realizamos la matriz de la multiplicación de p*q
W+0,2X+0Y+0,45Z = Z
W+X+Y+Z = 1
,3X+0,25Y+0,15Z = 0
X+0,35Y+0,15Z = 0
15X-0,6Y+0,25Z = 0 <- dejando todo igualado a 0
2X+0Y-0,55Z = 0
W+X+Y+Z-1 = 0
0.27 <- Resolviendo las ecuaciones
Y Z
0.25 0.15 0 0.000E+
0.35 0.15 0 -1.387779E-
-0.6 0.25 0 6.9388939E-
0 -0.55 0 0.0000E+
er in Payoff, according to historical accident rate?
$ 630,425.8 <- rta
W X Y Z
wo years will be charged for the new policy $ 530,000 (state
the first of the last two years you will be charged $ 517.
behavior of each state is given by the following cases of
ations of p * q, where p is the transition matrix and q the
l accident rate?
STATE TIGO COMCELMOVISTAR ETB
TIGO 0.25 0.15 0.35 0.
COMCEL 0.2 0.35 0.15 0.
MOVISTAR 0.35 0.2 0.2 0.
ETB 0.15 0.25 0.05 0.
UFF 0.15 0.25 0.3 0.
STATE TIGO COMCELMOVISTAR ETB UFF
TIGO 0.25 0.15 0.35 0.1 0.
COMCEL 0.2 0.35 0.15 0.1 0.
MOVISTAR 0.35 0.2 0.2 0.2 0.
ETB 0.15 0.25 0.05 0.25 0.
UFF 0.15 0.25 0.3 0.15 0.
TIGO COMCEL MOVISTAR ETB UFF
TIGO COMCEL MOVISTAR ETB UFF
TIGO COMCEL MOVISTAR ETB UFF
TIGO COMCEL MOVISTAR ETB UFF
Exercise 2. Markov chains (Initial state multiplication): In Colombia there are 5 main mobile operators such as Tigo, Comcel, Movistar, ETB and Uff, whic The following chart summarizes the odds that each client has to stay in their current operator o company. The current percentages of each operator in the current market are for Tigo 0.2 for Comcel 0.3, fo 0.1 and 0.1 for Uff (initial state). According to Table 2 by applying the Markovian criteria, solve the multiplication of the initial state by the probability matrix (transition matrix). Answer: a. Find the probability that each user stays with the mobile company for the 3 next periods.
UFF
Po
<- Prob. Iniciales <-Primer periodo <- Segundo periodo <- tercer periodo te multiplication): , Movistar, ETB and Uff, which we will call states. ay in their current operator or make a change of r Tigo 0.2 for Comcel 0.3, for Movistar 0.3, for ETB state). tiplication of the initial state vector (market share) matrix). Answer: the mobile company
TIGO COMCEL MOVISTAR ETB AVANTEL
UFF
mobile company for the nexts 4 periods. UFF Po 0.1 0. 0.1 0. 0 0. 0.2 0. 0.2 0. 0.2 0. UFF 0.2 (^) <- P. Iniciales UFF 0.11 <- Primer periodo UFF 0.124 <- Segundo periodo UFF state multiplication): go, Comcel, Movistar, ETB and Uff, which we will call as to stay in their current operator or make a change e for Tigo 0.1 for Comcel 0.2, for Movistar 0.3, for ETB ff (initial state). multiplication of the initial state vector (market share) on matrix). Answer:
COLOMBIANA PEPSI COLA FANTA
COLOMBIANA 40 20 10
PEPSI COLA 20 30 20
FANTA 40 20 20
COCA COLA 20 20 10
Matriz de transición COLOMBIANA PEPSI COLA FANTA COLOMBIANA 0.4 0.2 0. PEPSI COLA 0.2 0.3 0. FANTA 0.4 0.2 0. COCA COLA 0.2 0.2 0. COLOMBIANA PEPSI COLA FANTA 0.3 0.2 0. COLOMBIANA PEPSI COLA FANTA 0.28 0.22 0. COLOMBIANA PEPSI COLA FANTA 0.28 0.22 0. Exercise 4. Markov chains (Initial state multiplication): Suppose that 4 types of soft drinks are obtained in the market: Colombian, Pepsi Cola, Fanta an a person has bought Colombian there is a probability that they will continue to consume 40%, buy Pepsi Cola, 10% that Fanta buys and 30% that Coca Cola consumes; when the buyer curr Pepsi Cola there is a probability that he will continue to buy 30%, 20% buy Colombian, 20% tha and 30% Coca Cola; if Fanta is currently consumed, the likelihood of it continuing to be consum buy Colombian, 20% consume Pepsi Cola and 20% go to Coca Cola. If you currently consume probability that it will continue to consume is 50%, 20% buy Colombian, 20% that consumes Pe that is passed to Fanta. At present, each Colombian brand, Pepsi Cola, Fanta and Coca Cola have the following percen share respectively (30%, 20%, 10% and 40%) during week 3. According to the data by applying the Markovian criteria, solve the multiplication of the initial st share) by the probability matrix (transition matrix). Answer:
COCA COLA TOTAL
COCA COLA TOTAL
COCA COLA
0.4 (^) <- Tercera semana COCA COLA 0.37 <- Cuarta semana COCA COLA 0.36 <- Quinta semana multiplication): mbian, Pepsi Cola, Fanta and Coca Cola when continue to consume 40%, 20% of which will umes; when the buyer currently consumes % buy Colombian, 20% that Fanta consumes f it continuing to be consumed is 20%, 40% a. If you currently consume Coca Cola the ian, 20% that consumes Pepsi Cola and 10% a have the following percentages in market 0%) during week 3. ultiplication of the initial state vector (market n matrix). Answer:
BRAND 5 BRAND 6 TOTAL
hange to another for periodS 4, 5, 6 and period 7. BRAND 5 BRAND 6 0.18 0. 0.15 0. 0.2 0. 0.18 0. 0.15 0. 0.19 0. BRAND 6 0.20 <- Periodo 4 BRAND 6 0.13 <- Periodo 5 s (Initial state multiplication): Colombian market: Brand 1, Brand 2, Brand 3, Brand hows the odds that you continue to use the same r change it. t share respectively (20%, 15%, 17%, 15%, 13% y eek 4. solve the multiplication of the initial state vector x (transition matrix). Answer:
Table 1. Decision process for the commercialization of tha product
Manufacture 124 138 150 165
Subcontract 129 143 167 180
Buy 122 148 169 188
Lease 116 152 158 171
Leasing 119 131 167 172
Probabilities Ʃ = 0.25 0.3 0.3 0.
Manufacture NODO 2
Subcontract NODO 3
NODO 1
Buy NODO 4
Lease NODO 5
Leasing NODO 6
VEsIP 153.
VEcIP (0,25)129+(0,3)152+(0,3)169+(0,15)128 147.
VEIP 147,75-153,8 -6.
A company dedicated to manufacturing different turned parts must decide whether to
manufacture a new product at its main plant, or if it buys it from an outside supplier. The profits
depend on the demand of the product. Table 10 shows projected profits, in millions of pesos.
Decision
alternative
Demand low -
utility
Low average -
utility demand
High medium -
utility demand
High - demand
utility
FAVORABLE
ESTADO DE LA NATURALEZA ESTADO DE LA NATURALEZA
- BRAND 1 BRAND 2 BRAND 3 BRAND 4 BRAND
- BRAND 1 BRAND 2 BRAND 3 BRAND 4 BRAND
- BRAND
- BRAND
- P(F/low) = 0,25 P(D/low) = 0,
- P(F/low average) = 0,35 P(D/ low average) = 0,
- P(F/high medium) = 0,3 P(D/ high medium) = 0,
- P(F/high) = 0,32 P(D/high) = 0, - Probabilities Ʃ = 1 0.25 0.3 0.3 0. - 0.25 0.25 0.0625 0. - 0.3 0.35 0.105 0. - 0.3 0.3 0.09 0. - 0.15 0.32 0.048 0. - 0.3055 - 0.25 0.75 0.1875 0. DESFAVORABLE - 0.3 0.65 0.195 0. - 0.3 0.7 0.21 0. - 0.15 0.68 0.102 0. - 0.6945
- NODO - Manufacture NODO - 0.20 - 0.34 - 0.29 - 0.16 - Subcontract NODO - 0.20 - 0.34 - 0.29 - 0.16 - Buy NODO - 0.20 - 0.34 - 0.29 - 0.16 - Lease NODO - 0.20 - 0.34 - 0.29 - 0.16 - Leasing NODO - 0.20 - 0.34 - 0.29 - 0.16 - Manufacture NODO - 0.27 - 0.28 - 0.30 - 0.15
