The process of share price formation is studied in the article as well as a random process, and a model is developed that describes a random process that has characteristics close to the Brownian bridge, and realizes a multiplicative model of the bond price evolution with outpaced repayment time and normal value. The definition of a random process of forming a share price through a geometric Brownian bridge is also given. Since the Ukrainian insurance market is at the initial stage of development, and the country's economy is unstable, insurance companies need practical and reliable tools for calculating and forecasting the expected return on investment activity. And especially urgent for this particular type of activity is the issue of breakeven investment, as insurance companies can’t afford risky investment because of the specifics of their activities. As a research result, the level of investing in a risk-free asset for an insurance company of a cumulative type is calculated.