Displaying Values of Fuction at end of Period by Grid

Question

My intention is to place the values of two function into a small box within my chart. To be more precise I have two vectors.

A meanvector which shows the average value of all simulated stochastic processes and an other vector, namely thresholdedmeanvector which represents the average value only of those processes which remain beyond the in the function defined threshold.

So I just want a box somewhere in the chart with the titles “mean of all stochastic processes” and below the displayed value of this vector at the end of the period (which is defined as “time” in the code) and the title “mean of all stochastic processes beyond the threshold” next to it, which also displays the value of the average of the stochastic processes which remained beyond the threshold at the end of the period (again defined as “time”)

In the first step, I tried just to display the mean value of all stochastic processes somewhere in the chart. Therefore I uses the Grid Function, but I am struggling with it. I think I have placed it somewhere in a wrong position in the function, but I am not sure.

Does anyone of you have a suggestion where I should place the Grid Function or an easier alternative? Thanks, and below you can find the underlying code.

Manipulate[SeedRandom[seed]; meanvector := Mean[assets]; 
 assets = Table[RandomFunction[
GeometricBrownianMotionProcess[μ, σ, S0], {0, time, 0.1}]["Path"], {P}];


 processes = Transpose[assets[[#]]][[2]] & /@ Range@Length[assets]; 
 processesposition = Flatten[Position[
Min[processes[[#]]] & /@ Range@Length[assets], _?(# > threshold &)]]; 



 thresholdedassets = assets[[#]] & /@ processesposition; 
 thresholdedmeanvector = Mean[thresholdedassets];


 (*vector of meanvector*)
 vmv = TableView[{meanvector, NumberForm[meanvector, {4, 5}]}, {0, time}]; 

 vmv = Prepend[
   vmv, {"Mean Value of all Assets and the end of the period"}];

 G1 := ListLogPlot[assets, GridLines -> {{}, {threshold}}, 
   GridLinesStyle -> Directive[Green, Thick], Joined -> True, 
   AxesLabel -> {"Time", "St"}, 
   PlotLabel -> Style["Forecasted Stock Price\n (Brownian Motion)", Bold], 
   PlotRange -> All, PlotStyle -> Directive[{Thin, Lighter@Gray}]];

 G2 := ListLogPlot[{meanvector, thresholdedmeanvector}, 
   Joined -> True, 
   PlotStyle -> {Directive[{Thick, Darker@Red}], 
     Directive[{Thick, Darker@Blue}]}];

 (*introduction of Grid Box for meanvector*)

 Grid[{Text@ Grid[vmv, Alignment -> Left, Frame -> All,ItemStyle -> {Automatic, {Bold}}],



   Show[G1, G2]}],

 {{S0, 100, "Initial Stock Value"}, 1, 500, 0.5, Appearance -> "Labeled"}, 
 {{μ, 0.08, "Drift μ"}, 0.01, 0.2, 0.01, Appearance -> "Labeled"}, 
 {{σ, 0.2, "Standard Deviation σ"}, 0.01, 1, 0.05, 
  Appearance -> "Labeled"},
 {{P, 6, "Paths"}, 1, 20, 1,Appearance -> "Labeled"}, 
 {{time, 10, "Time t"}, 1, 20, 1, Appearance -> "Labeled"},  
 {{threshold, 75, "Debt Level"}, 1, 500, Appearance -> "Labeled"},  
 Delimiter, {{seed, 0, ""},Button["randomize", seed = RandomInteger[2^64 - 1]] &},  

 Button["Set Initial Values", {S0 = 100, μ = 0.08, σ = 
    0.20, P = 6, time = 10, threshold = 75}, ImageSize -> 150], 
 ControlPlacement -> Left]

Answer 1

Milan, the easiest way to do it is by using Dynamic[].

Manipulate[SeedRandom[seed];
meanvector := Mean[assets];
assets = Table[RandomFunction[GeometricBrownianMotionProcess[μ, σ, S0], {0, time, 0.1}]["Path"], {P}];
processes = Transpose[assets[[#]]][[2]] & /@ Range@Length[assets];
processesposition=Flatten[Position[Min[processes[[#]]]&/@Range@Length[assets], _?(# > watermark &)]];
watermarkedassets = assets[[#]] & /@ processesposition;
watermarkedmeanvector = Mean[watermarkedassets];
G1 := ListLogPlot[assets, GridLines -> {{}, {watermark}},GridLinesStyle -> Directive[Green, Thick], Joined -> True, AxesLabel -> {"Time", "St"}, PlotLabel -> Style["Forecasted Stock Price\n (Brownian Motion)", Bold], PlotRange -> All, PlotStyle -> Directive[{Thin, Lighter@Gray}]];
G2 := ListLogPlot[{meanvector, watermarkedmeanvector},Joined -> True, PlotStyle -> {Directive[{Thick, Darker@Red}], Directive[{Thick, Darker@Blue}]}];
Show[G1, G2], 
{{S0, 100, "Initial Stock Value"}, 1, 500, 0.5, Appearance -> "Labeled"}, 
{{μ, 0.08, "Drift μ"}, 0.01, 0.2, 0.01, Appearance -> "Labeled"}, 
{{σ, 0.2, "Standard Deviation σ"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
{{P, 6, "Paths"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{time, 10, "Time t"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{watermark, 75, "Watermark"}, 1, 500, Appearance -> "Labeled"}, 
{{seed, 1, "New Random Case"}, 1, 100, 1}, 
Button["Set Initial Values", {S0 = 100, μ = 0.08, σ = 0.20, P = 6, time = 10, watermark = 75}, ImageSize -> 150], 
Dynamic["Mean watermarked processes = "<>ToString[watermarkedmeanvector[[-1]][[2]]]],
Dynamic["Mean of all processes = "<>ToString[meanvector[[-1]][[2]]]],    
ControlPlacement -> Left]