Double v = (Double.parseDouble(data[2]));
if (v<0){
//do whatever?
}

I suggest you step through your code using a debugger and you would see how your values are actually changing.

Your negative interest is interest_neg = -0.002. which you multiply by your amount.

Say you have the following situation

double balance = -100;
if ( balance >= 0 ) balance *= interest_pos;
else balance *= interest_neg; // balance = -100 * -0.002 = +0.2

A negative interest doesn't make any sense of this value as you can see. If I had a million dollar debt, the next month I would have $200. The more in debt I am the more money I will have next month.

So whenever you have a negative balance you are making it positive again. Perhaps your negative interest should be 1.002, similar to your positive interest.

else balance *= interest_neg; // balance = -100 * 1.002 = -100.2

Your c12 and fileSize are most likely ints (+1 Tomasz). Java multiplies the ints, which overflows, becoming negative, and then stores that negative value in your double. Cast c12 and fileSize to double before multiplying:

double c12 = 1700, fileSize = 1944038;
System.out.println(c12 * fileSize);

produces:

3.3048646E9

This can be achieved without relying on exceptions to control the flow of your program, which is generally a bad idea - see discussion here

else {   
    // using a tempBidAmount as I don't have enough context to know whether
    // I could just assign the output of parseUserDouble directly to bidAmount
    // without causing issues
    Double tempBidAmount = parseUserDouble(messageToServer);

    if (tempBidAmount != null && tempBidAmount > 0.0) {
        bidAmount = tempBidAmount;
        output.println(selectedItemCode + bidAmount);
    } else {
        fromServer.setText("Invalid Request!" + USER_PROMPT);
    }
}
toServer.setText("");

....

private Double parseUserDouble(Sting userInput) {
    try {
        return Double.parseDouble(userInput);
    }
    catch (NumberFormatException numfEx) {
        // consider logging here        
    }
    return null;
}