minimax

compare the minimax

a<-c(0,10,20,-10,-20,
     0,15,30,-5,-10,
     0,100,200,-100,-200,
     -10,300,1000,-300,-1000)
# index, alpha, leverage, structure payoff mat

a <- matrix(a,byrow = T,nrow = 4)
rownames(a) <- c('index','alpha','leverage','structure')
colnames(a) <- c('keep','up','roarup','down','dropdown')
regret_a<-apply(a, 2, max)
(regret<-t(apply(a, 1, function(x) regret_a - x)))

##           keep  up roarup down dropdown
## index        0 290    980    5       10
## alpha        0 285    970    0        0
## leverage     0 200    800   95      190
## structure   10   0      0  295      990

bulk <- c(0.1,.5,.3,.07,.03) #bulk market
bear <- c(0.1,.07,.03,.5,.3) #bear market
calm <- c(0.5,0.2,0.05,0.2,0.05) 

library(knitr)

## Warning: package 'knitr' was built under R version 3.2.5

result<-data.frame(
  maxmin=apply(a, 1, min),
  minmaxReg=apply(regret, 1, max),
  maxMean_bulk=a%*%bulk,
  maxMean_bear=a%*%bear,
  maxMean_calm=a%*%calm,
  minMeanReg_bulk=regret%*%bulk,
  minMeanReg_bear=regret%*%bear,
  minMeanReg_calm=regret%*%calm
)

r<-rbind(result,rownames(result)[c(which.max(result$maxmin),
                              which.min(result$minmaxReg),
                              which.max(result$maxMean_bulk),
                              which.max(result$maxMean_bear),
                              which.max(result$maxMean_calm),
                              which.min(result$minMeanReg_bulk),
                              which.min(result$minMeanReg_bear),
                              which.min(result$minMeanReg_calm))])

kable(r)

	maxmin	minmaxReg	maxMean_bulk	maxMean_bear	maxMean_calm	minMeanReg_bulk	minMeanReg_bear	minMeanReg_calm
index	-20	980	9.7	-9.7	0	439.65	55.2	108.5
alpha	-10	970	15.85	-3.55	3	433.5	49.05	105.5
leverage	-200	800	97	-97	0	352.35	142.5	108.5
structure	-1000	990	398	-400	-5	51.35	445.5	113.5
5	alpha	leverage	structure	alpha	alpha	structure	alpha	alpha