Which regression model should I apply?

Dear all,

I want to do an empirical analysis on the risk-return characteristics of venture capital investments across industries applying a discrete binomial tree model. Therefore, I want to do a multiple regression. However, I am struggling with the decision which regression model I should apply.

Here my issue: Since VC investments are staged investments (I am also assuming a discrete binomial model), the risk-neutral probability varies from stage to stage. Logically, I want to use the risk-neutral probability as the dependent variable, and among others, the time between the financing rounds, the total number of financing rounds so far, the amount of capital injected and some industry variables as the independent variables. My question now is: Which regression model can I apply to account for and analyze the fact that - as I am assuming - the dependent variable increases over time? E.g. would a Cox regression make sense in this context if I only have the data of successful ventures -> I acutally do not think so.

I would be very happy if you can help me with this.

Many thanks,