Table 1 Optimal solutions with two... | Emerald Publishing

Table 1

Optimal solutions with two different situations

Maximizing the sum of the benefits of the insurer and reinsurer
$μ = 9.294, σ = 1.627, γ_{2} = 2$
$γ_{1}$	2	4	6	8
$P^{*}$	16,600	23,200	26,800	29,100
$M^{*}$	24,200	17,600	14,000	11,700
$E^{*} (Y)$	$- 0.5375 \times 10^{10}$	$- 0.2706 \times 10^{10}$	$- 0.1810 \times 10^{10}$	$- 0.1360 \times 10^{10}$
$P$	10,000	10,000	10,000	10,000
$M^{*}$	30,846	30,846	30,846	30,846
$E^{*} (Y)$	$- 0.5389 \times 10^{10}$	$- 0.2735 \times 10^{10}$	$- 0.1823 \times 10^{10}$	$- 0.1367 \times 10^{10}$

Maximizing the sum of the benefits of the insurer and reinsurer
$μ = 9.294, σ = 1.627, γ_{2} = 2$
$γ_{1}$	2	4	6	8
$P^{*}$	16,600	23,200	26,800	29,100
$M^{*}$	24,200	17,600	14,000	11,700
$E^{*} (Y)$	$- 0.5375 \times 10^{10}$	$- 0.2706 \times 10^{10}$	$- 0.1810 \times 10^{10}$	$- 0.1360 \times 10^{10}$
$P$	10,000	10,000	10,000	10,000
$M^{*}$	30,846	30,846	30,846	30,846
$E^{*} (Y)$	$- 0.5389 \times 10^{10}$	$- 0.2735 \times 10^{10}$	$- 0.1823 \times 10^{10}$	$- 0.1367 \times 10^{10}$

Maximizing the sum of the benefits of the insurer and reinsurer
$μ = 9.294, σ = 1.627, γ_{2} = 4$
$γ_{1}$	2	4	6	8
$P^{*}$	10,700	16,600	20,500	23,200
$M^{*}$	30,100	24,200	20,300	17,600
$E^{*} (Y)$	$- 0.5339 \times 10^{10}$	$- 0.2688 \times 10^{10}$	$- 0.1799 \times 10^{10}$	$- 0.1353 \times 10^{10}$
$P$	10,000	10,000	10,000	10,000
$M^{*}$	30,846	30,846	30,846	30,846
$E^{*} (Y)$	$- 0.5339 \times 10^{10}$	$- 0.2694 \times 10^{10}$	$- 0.1813 \times 10^{10}$	$- 0.1367 \times 10^{10}$

Maximizing the sum of the benefits of the insurer and reinsurer
$μ = 9.294, σ = 1.627, γ_{2} = 4$
$γ_{1}$	2	4	6	8
$P^{*}$	10,700	16,600	20,500	23,200
$M^{*}$	30,100	24,200	20,300	17,600
$E^{*} (Y)$	$- 0.5339 \times 10^{10}$	$- 0.2688 \times 10^{10}$	$- 0.1799 \times 10^{10}$	$- 0.1353 \times 10^{10}$
$P$	10,000	10,000	10,000	10,000
$M^{*}$	30,846	30,846	30,846	30,846
$E^{*} (Y)$	$- 0.5339 \times 10^{10}$	$- 0.2694 \times 10^{10}$	$- 0.1813 \times 10^{10}$	$- 0.1367 \times 10^{10}$

Maximizing the product of the benefits of the insurer and reinsurer
$μ = 9.294, σ = 1.627, γ_{2} = 2$
$γ_{1}$	2	4	6	8
$P^{*}$	22,900	22,900	22,900	22,900
$M^{*}$	17,946	17,946	17,946	17,946
$E^{*} (Y)$	$3.8017 \times 10^{15}$	$1.9004 \times 10^{15}$	$1.2667 \times 10^{15}$	$0.9498 \times 10^{15}$
$P$	10,000	10,000	10,000	10,000
$M^{*}$	30,846	30,846	30,846	30,846
$E^{*} (Y)$	$2.7892 \times 10^{15}$	$1.3941 \times 10^{15}$	$0.9290 \times 10^{15}$	$0.6965 \times 10^{15}$

Maximizing the product of the benefits of the insurer and reinsurer
$μ = 9.294, σ = 1.627, γ_{2} = 2$
$γ_{1}$	2	4	6	8
$P^{*}$	22,900	22,900	22,900	22,900
$M^{*}$	17,946	17,946	17,946	17,946
$E^{*} (Y)$	$3.8017 \times 10^{15}$	$1.9004 \times 10^{15}$	$1.2667 \times 10^{15}$	$0.9498 \times 10^{15}$
$P$	10,000	10,000	10,000	10,000
$M^{*}$	30,846	30,846	30,846	30,846
$E^{*} (Y)$	$2.7892 \times 10^{15}$	$1.3941 \times 10^{15}$	$0.9290 \times 10^{15}$	$0.6965 \times 10^{15}$

Maximizing the product of the benefits of the insurer and reinsurer
$μ = 9.294, σ = 1.627, γ_{2} = 4$
$γ_{1}$	2	4	6	8
$P^{*}$	22,900	22,900	22,900	22,900
$M^{*}$	17,946	17,946	17,946	17,946
$E^{*} (Y)$	$1.9004 \times 10^{15}$	$0.95 \times 10^{15}$	$0.6332 \times 10^{15}$	$0.4748 \times 10^{15}$
$P$	10,000	10,000	10,000	10,000
$M^{*}$	30,846	30,846	30,846	30,846
$E^{*} (Y)$	$1.3944 \times 10^{15}$	$0.6969 \times 10^{15}$	$0.4644 \times 10^{15}$	$0.3482 \times 10^{15}$

Maximizing the product of the benefits of the insurer and reinsurer
$μ = 9.294, σ = 1.627, γ_{2} = 4$
$γ_{1}$	2	4	6	8
$P^{*}$	22,900	22,900	22,900	22,900
$M^{*}$	17,946	17,946	17,946	17,946
$E^{*} (Y)$	$1.9004 \times 10^{15}$	$0.95 \times 10^{15}$	$0.6332 \times 10^{15}$	$0.4748 \times 10^{15}$
$P$	10,000	10,000	10,000	10,000
$M^{*}$	30,846	30,846	30,846	30,846
$E^{*} (Y)$	$1.3944 \times 10^{15}$	$0.6969 \times 10^{15}$	$0.4644 \times 10^{15}$	$0.3482 \times 10^{15}$

Source(s): Authors' calculation