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Fair Value of Financial Instruments - Fair Value of Invested Assets (Details) - USD ($)
Jun. 30, 2018
Dec. 31, 2017
Jun. 30, 2017
Dec. 31, 2016
Fixed maturity investments available for sale:        
U.S. treasury securities $ 10,512,602 $ 7,454,225    
Corporate securities 32,326,331 28,657,640    
Agency mortgage-backed securities 21,929,549 21,737,589    
Held to maturity fixed maturity investments:        
Certificates of deposit 20,602,000 28,098,000    
Total fixed maturities 85,370,482 85,947,454    
Cash, cash equivalents, and restricted cash 7,835,200 9,366,944 $ 15,480,020 $ 22,602,982
Short-term investments, at fair value 200,000 1,847,778    
Total financial instruments at fair value 93,405,682 97,162,176    
Level 1        
Fixed maturity investments available for sale:        
U.S. treasury securities 10,512,602 7,454,225    
Corporate securities 0 0    
Agency mortgage-backed securities 0 0    
Held to maturity fixed maturity investments:        
Certificates of deposit 0 0    
Total fixed maturities 10,512,602 7,454,225    
Cash, cash equivalents, and restricted cash 7,835,200 9,366,944    
Short-term investments, at fair value 200,000 1,847,778    
Total financial instruments at fair value 18,547,802 18,668,947    
Level 2        
Fixed maturity investments available for sale:        
U.S. treasury securities 0 0    
Corporate securities 32,326,331 28,657,640    
Agency mortgage-backed securities 21,929,549 21,737,589    
Held to maturity fixed maturity investments:        
Certificates of deposit 20,602,000 28,098,000    
Total fixed maturities 74,857,880 78,493,229    
Cash, cash equivalents, and restricted cash 0 0    
Short-term investments, at fair value 0 0    
Total financial instruments at fair value 74,857,880 78,493,229    
Level 3        
Fixed maturity investments available for sale:        
U.S. treasury securities 0 0    
Corporate securities 0 0    
Agency mortgage-backed securities 0 0    
Held to maturity fixed maturity investments:        
Certificates of deposit 0 0    
Total fixed maturities 0 0    
Cash, cash equivalents, and restricted cash 0 0    
Short-term investments, at fair value 0 0    
Total financial instruments at fair value $ 0 $ 0